Homotopy groups of spheres (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Homotopy groups of spheres" in English language version.

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Hatcher 2002, p. xii. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Hatcher 2002, Example 0.3, p. 6. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Hatcher 2002, p. 129. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Hatcher 2002, p. 28. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Hatcher 2002, p. 3. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Miranda 1995, pp. 123–125. Miranda, Rick (1995), Algebraic curves and Riemann surfaces, Graduate Studies in Mathematics, vol. 5, Providence, Rhode Island: American Mathematical Society, doi:10.1090/gsm/005, ISBN 0-8218-0268-2, MR 1326604
Hu 1959, p. 107. Hu, Sze-tsen (1959), Homotopy theory, Pure and Applied Mathematics, vol. 8, New York & London: Academic Press, MR 0106454
Hatcher 2002, p. 29. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
See, e.g., Homotopy type theory 2013, Section 8.1, " ${\textstyle \pi _{1}(S^{1})}$ ". Homotopy type theory—univalent foundations of mathematics, The Univalent Foundations Program and Institute for Advanced Study, 2013, MR 3204653
Hatcher 2002, p. 348. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Hatcher 2002, p. 349. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Hatcher 2002, p. 61. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Walschap 2004, p. 90. Walschap, Gerard (2004), "Chapter 3: Homotopy groups and bundles over spheres", Metric structures in differential geometry, Graduate Texts in Mathematics, vol. 224, Springer-Verlag, New York, doi:10.1007/978-0-387-21826-7, ISBN 0-387-20430-X, MR 2045823
Hatcher 2002, p. 361. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Hatcher 2002, p. 342. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Hatcher 2002, Stable homotopy groups, pp. 385–393. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Hatcher 2002. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Scorpan 2005. Scorpan, Alexandru (2005), The wild world of 4-manifolds, American Mathematical Society, ISBN 978-0-8218-3749-8, MR 2136212.
Serre 1951. Serre, Jean-Pierre (1951), "Homologie singulière des espaces fibrés. Applications", Annals of Mathematics, Second Series, 54 (3): 425–505, doi:10.2307/1969485, JSTOR 1969485, MR 0045386.
Cohen, Moore & Neisendorfer 1979. Cohen, Frederick R.; Moore, John C.; Neisendorfer, Joseph A. (November 1979), "The double suspension and exponents of the homotopy groups of spheres", Annals of Mathematics, Second Series, 110 (3): 549–565, doi:10.2307/1971238, JSTOR 1971238, MR 0554384.
Ravenel 2003, p. 4. Ravenel, Douglas C. (2003), Complex cobordism and stable homotopy groups of spheres (2nd ed.), AMS Chelsea, ISBN 978-0-8218-2967-7, MR 0860042.
Serre 1952. Serre, Jean-Pierre (1952), "Sur la suspension de Freudenthal", Comptes Rendus de l'Académie des Sciences, Série I, 234, Paris: 1340–1342, ISSN 0764-4442, MR 0046048.
Ravenel 2003, p. 25. Ravenel, Douglas C. (2003), Complex cobordism and stable homotopy groups of spheres (2nd ed.), AMS Chelsea, ISBN 978-0-8218-2967-7, MR 0860042.
Nishida 1973. Nishida, Goro (1973), "The nilpotency of elements of the stable homotopy groups of spheres", Journal of the Mathematical Society of Japan, 25 (4): 707–732, doi:10.2969/jmsj/02540707, hdl:2433/220059, ISSN 0025-5645, MR 0341485.
Toda 1962. Toda, Hirosi (1962), Composition methods in homotopy groups of spheres, Annals of Mathematics Studies, vol. 49, Princeton University Press, ISBN 978-0-691-09586-8, MR 0143217 {{citation}}: ISBN / Date incompatibility (help).
Cohen 1968. Cohen, Joel M. (1968), "The decomposition of stable homotopy", Annals of Mathematics, Second Series, 87 (2): 305–320, doi:10.2307/1970586, JSTOR 1970586, MR 0231377, PMC 224450, PMID 16591550.
Ravenel 2003. Ravenel, Douglas C. (2003), Complex cobordism and stable homotopy groups of spheres (2nd ed.), AMS Chelsea, ISBN 978-0-8218-2967-7, MR 0860042.
Ravenel 2003, pp. 67–74. Ravenel, Douglas C. (2003), Complex cobordism and stable homotopy groups of spheres (2nd ed.), AMS Chelsea, ISBN 978-0-8218-2967-7, MR 0860042.
Ravenel 2003, Chapter 5. Ravenel, Douglas C. (2003), Complex cobordism and stable homotopy groups of spheres (2nd ed.), AMS Chelsea, ISBN 978-0-8218-2967-7, MR 0860042.
Kochman 1990. Kochman, Stanley O. (1990), Stable homotopy groups of spheres. A computer-assisted approach, Lecture Notes in Mathematics, vol. 1423, Berlin: Springer-Verlag, doi:10.1007/BFb0083795, ISBN 978-3-540-52468-7, MR 1052407 Also see the corrections in (Kochman & Mahowald 1995)
Isaksen 2019. Isaksen, Daniel C. (2019), "Stable Stems", Memoirs of the American Mathematical Society, 262 (1269), doi:10.1090/memo/1269, ISBN 978-1-4704-3788-6, MR 4046815.
Wang & Xu 2017. Wang, Guozhen; Xu, Zhouli (2017), "The triviality of the 61-stem in the stable homotopy groups of spheres", Annals of Mathematics, 186 (2): 501–580, arXiv:1601.02184, doi:10.4007/annals.2017.186.2.3, MR 3702672, S2CID 119147703.
Berrick et al. 2006. Berrick, A. J.; Cohen, Frederick R.; Wong, Yan Loi; Wu, Jie (2006), "Configurations, braids, and homotopy groups", Journal of the American Mathematical Society, 19 (2): 265–326, doi:10.1090/S0894-0347-05-00507-2, MR 2188127.
Fine & Rosenberger 1997. Fine, Benjamin; Rosenberger, Gerhard (1997), "8.1 Winding Number and Proof Five", The Fundamental Theorem of Algebra, Undergraduate Texts in Mathematics, Springer-Verlag, New York, pp. 134–136, doi:10.1007/978-1-4612-1928-6, ISBN 0-387-94657-8, MR 1454356
Hatcher 2002, p. 32. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Kervaire & Milnor 1963. Kervaire, Michel A.; Milnor, John W. (1963), "Groups of homotopy spheres: I", Annals of Mathematics, 77 (3): 504–537, doi:10.2307/1970128, JSTOR 1970128, MR 0148075.
Barratt, Jones & Mahowald 1984. Barratt, Michael G.; Jones, John D. S.; Mahowald, Mark E. (1984), "Relations amongst Toda brackets and the Kervaire invariant in dimension 62", Journal of the London Mathematical Society, 30 (3): 533–550, CiteSeerX 10.1.1.212.1163, doi:10.1112/jlms/s2-30.3.533, MR 0810962.
Deitmar 2006. Deitmar, Anton (2006), "Remarks on zeta functions and K-theory over F₁", Proceedings of the Japan Academy, Series A, Mathematical Sciences, 82 (8): 141–146, arXiv:math/0605429, doi:10.3792/pjaa.82.141, ISSN 0386-2194, MR 2279281.
These tables are based on the table of homotopy groups of spheres in Toda (1962). Toda, Hirosi (1962), Composition methods in homotopy groups of spheres, Annals of Mathematics Studies, vol. 49, Princeton University Press, ISBN 978-0-691-09586-8, MR 0143217 {{citation}}: ISBN / Date incompatibility (help).
Fuks 2001. The 2-components can be found in Isaksen, Wang & Xu (2023), and the 3- and 5-components in Ravenel (2003). Fuks, Dmitry B. (2001) [1994], "Spheres, homotopy groups of the", Encyclopedia of Mathematics, EMS Press. Isaksen, Daniel C.; Wang, Guozhen; Xu, Zhouli (2023), "Stable homotopy groups of spheres: from dimension 0 to 90", Publications mathématiques de l'IHÉS, 137: 107–243, arXiv:2001.04511, doi:10.1007/s10240-023-00139-1. Ravenel, Douglas C. (2003), Complex cobordism and stable homotopy groups of spheres (2nd ed.), AMS Chelsea, ISBN 978-0-8218-2967-7, MR 0860042.

arxiv.org

Isaksen, Wang & Xu 2023. Isaksen, Daniel C.; Wang, Guozhen; Xu, Zhouli (2023), "Stable homotopy groups of spheres: from dimension 0 to 90", Publications mathématiques de l'IHÉS, 137: 107–243, arXiv:2001.04511, doi:10.1007/s10240-023-00139-1.
Wang & Xu 2017. Wang, Guozhen; Xu, Zhouli (2017), "The triviality of the 61-stem in the stable homotopy groups of spheres", Annals of Mathematics, 186 (2): 501–580, arXiv:1601.02184, doi:10.4007/annals.2017.186.2.3, MR 3702672, S2CID 119147703.
Gheorghe, Wang & Xu 2021. Gheorghe, Bogdan; Wang, Guozhen; Xu, Zhouli (2021), "The special fiber of the motivic deformation of the stable homotopy category is algebraic", Acta Mathematica, 226 (2): 319–407, arXiv:1809.09290, doi:10.4310/ACTA.2021.v226.n2.a2, S2CID 119303902.
Deitmar 2006. Deitmar, Anton (2006), "Remarks on zeta functions and K-theory over F₁", Proceedings of the Japan Academy, Series A, Mathematical Sciences, 82 (8): 141–146, arXiv:math/0605429, doi:10.3792/pjaa.82.141, ISSN 0386-2194, MR 2279281.
Fuks 2001. The 2-components can be found in Isaksen, Wang & Xu (2023), and the 3- and 5-components in Ravenel (2003). Fuks, Dmitry B. (2001) [1994], "Spheres, homotopy groups of the", Encyclopedia of Mathematics, EMS Press. Isaksen, Daniel C.; Wang, Guozhen; Xu, Zhouli (2023), "Stable homotopy groups of spheres: from dimension 0 to 90", Publications mathématiques de l'IHÉS, 137: 107–243, arXiv:2001.04511, doi:10.1007/s10240-023-00139-1. Ravenel, Douglas C. (2003), Complex cobordism and stable homotopy groups of spheres (2nd ed.), AMS Chelsea, ISBN 978-0-8218-2967-7, MR 0860042.

books.google.com

Miranda 1995, pp. 123–125. Miranda, Rick (1995), Algebraic curves and Riemann surfaces, Graduate Studies in Mathematics, vol. 5, Providence, Rhode Island: American Mathematical Society, doi:10.1090/gsm/005, ISBN 0-8218-0268-2, MR 1326604
Hu 1959, p. 107. Hu, Sze-tsen (1959), Homotopy theory, Pure and Applied Mathematics, vol. 8, New York & London: Academic Press, MR 0106454

cornell.edu

pi.math.cornell.edu

Hatcher 2002, p. xii. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Hatcher 2002, Example 0.3, p. 6. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Hatcher 2002, p. 129. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Hatcher 2002, p. 28. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Hatcher 2002, p. 3. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Hatcher 2002, p. 29. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Hatcher 2002, p. 348. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Hatcher 2002, p. 349. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Hatcher 2002, p. 61. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Hatcher 2002, p. 361. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Hatcher 2002, p. 342. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Hatcher 2002, Stable homotopy groups, pp. 385–393. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Hatcher 2002. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.
Hatcher 2002, p. 32. Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1, MR 1867354.

doi.org

Isaksen, Wang & Xu 2023. Isaksen, Daniel C.; Wang, Guozhen; Xu, Zhouli (2023), "Stable homotopy groups of spheres: from dimension 0 to 90", Publications mathématiques de l'IHÉS, 137: 107–243, arXiv:2001.04511, doi:10.1007/s10240-023-00139-1.
Miranda 1995, pp. 123–125. Miranda, Rick (1995), Algebraic curves and Riemann surfaces, Graduate Studies in Mathematics, vol. 5, Providence, Rhode Island: American Mathematical Society, doi:10.1090/gsm/005, ISBN 0-8218-0268-2, MR 1326604
Hopf 1931. Hopf, Heinz (1931), "Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche", Mathematische Annalen, 104 (1): 637–665, doi:10.1007/BF01457962, S2CID 123533891.
Walschap 2004, p. 90. Walschap, Gerard (2004), "Chapter 3: Homotopy groups and bundles over spheres", Metric structures in differential geometry, Graduate Texts in Mathematics, vol. 224, Springer-Verlag, New York, doi:10.1007/978-0-387-21826-7, ISBN 0-387-20430-X, MR 2045823
Serre 1951. Serre, Jean-Pierre (1951), "Homologie singulière des espaces fibrés. Applications", Annals of Mathematics, Second Series, 54 (3): 425–505, doi:10.2307/1969485, JSTOR 1969485, MR 0045386.
Cohen, Moore & Neisendorfer 1979. Cohen, Frederick R.; Moore, John C.; Neisendorfer, Joseph A. (November 1979), "The double suspension and exponents of the homotopy groups of spheres", Annals of Mathematics, Second Series, 110 (3): 549–565, doi:10.2307/1971238, JSTOR 1971238, MR 0554384.
Nishida 1973. Nishida, Goro (1973), "The nilpotency of elements of the stable homotopy groups of spheres", Journal of the Mathematical Society of Japan, 25 (4): 707–732, doi:10.2969/jmsj/02540707, hdl:2433/220059, ISSN 0025-5645, MR 0341485.
Cohen 1968. Cohen, Joel M. (1968), "The decomposition of stable homotopy", Annals of Mathematics, Second Series, 87 (2): 305–320, doi:10.2307/1970586, JSTOR 1970586, MR 0231377, PMC 224450, PMID 16591550.
Kochman 1990. Kochman, Stanley O. (1990), Stable homotopy groups of spheres. A computer-assisted approach, Lecture Notes in Mathematics, vol. 1423, Berlin: Springer-Verlag, doi:10.1007/BFb0083795, ISBN 978-3-540-52468-7, MR 1052407 Also see the corrections in (Kochman & Mahowald 1995)
Isaksen 2019. Isaksen, Daniel C. (2019), "Stable Stems", Memoirs of the American Mathematical Society, 262 (1269), doi:10.1090/memo/1269, ISBN 978-1-4704-3788-6, MR 4046815.
Wang & Xu 2017. Wang, Guozhen; Xu, Zhouli (2017), "The triviality of the 61-stem in the stable homotopy groups of spheres", Annals of Mathematics, 186 (2): 501–580, arXiv:1601.02184, doi:10.4007/annals.2017.186.2.3, MR 3702672, S2CID 119147703.
Gheorghe, Wang & Xu 2021. Gheorghe, Bogdan; Wang, Guozhen; Xu, Zhouli (2021), "The special fiber of the motivic deformation of the stable homotopy category is algebraic", Acta Mathematica, 226 (2): 319–407, arXiv:1809.09290, doi:10.4310/ACTA.2021.v226.n2.a2, S2CID 119303902.
Berrick et al. 2006. Berrick, A. J.; Cohen, Frederick R.; Wong, Yan Loi; Wu, Jie (2006), "Configurations, braids, and homotopy groups", Journal of the American Mathematical Society, 19 (2): 265–326, doi:10.1090/S0894-0347-05-00507-2, MR 2188127.
Fine & Rosenberger 1997. Fine, Benjamin; Rosenberger, Gerhard (1997), "8.1 Winding Number and Proof Five", The Fundamental Theorem of Algebra, Undergraduate Texts in Mathematics, Springer-Verlag, New York, pp. 134–136, doi:10.1007/978-1-4612-1928-6, ISBN 0-387-94657-8, MR 1454356
Kervaire & Milnor 1963. Kervaire, Michel A.; Milnor, John W. (1963), "Groups of homotopy spheres: I", Annals of Mathematics, 77 (3): 504–537, doi:10.2307/1970128, JSTOR 1970128, MR 0148075.
Barratt, Jones & Mahowald 1984. Barratt, Michael G.; Jones, John D. S.; Mahowald, Mark E. (1984), "Relations amongst Toda brackets and the Kervaire invariant in dimension 62", Journal of the London Mathematical Society, 30 (3): 533–550, CiteSeerX 10.1.1.212.1163, doi:10.1112/jlms/s2-30.3.533, MR 0810962.
Deitmar 2006. Deitmar, Anton (2006), "Remarks on zeta functions and K-theory over F₁", Proceedings of the Japan Academy, Series A, Mathematical Sciences, 82 (8): 141–146, arXiv:math/0605429, doi:10.3792/pjaa.82.141, ISSN 0386-2194, MR 2279281.
Fuks 2001. The 2-components can be found in Isaksen, Wang & Xu (2023), and the 3- and 5-components in Ravenel (2003). Fuks, Dmitry B. (2001) [1994], "Spheres, homotopy groups of the", Encyclopedia of Mathematics, EMS Press. Isaksen, Daniel C.; Wang, Guozhen; Xu, Zhouli (2023), "Stable homotopy groups of spheres: from dimension 0 to 90", Publications mathématiques de l'IHÉS, 137: 107–243, arXiv:2001.04511, doi:10.1007/s10240-023-00139-1. Ravenel, Douglas C. (2003), Complex cobordism and stable homotopy groups of spheres (2nd ed.), AMS Chelsea, ISBN 978-0-8218-2967-7, MR 0860042.

encyclopediaofmath.org

Fuks 2001. Fuks, Dmitry B. (2001) [1994], "Spheres, homotopy groups of the", Encyclopedia of Mathematics, EMS Press.
Mahowald 2001. Mahowald, Mark (2001) [1994], "EHP spectral sequence", Encyclopedia of Mathematics, EMS Press.
Fuks 2001. The 2-components can be found in Isaksen, Wang & Xu (2023), and the 3- and 5-components in Ravenel (2003). Fuks, Dmitry B. (2001) [1994], "Spheres, homotopy groups of the", Encyclopedia of Mathematics, EMS Press. Isaksen, Daniel C.; Wang, Guozhen; Xu, Zhouli (2023), "Stable homotopy groups of spheres: from dimension 0 to 90", Publications mathématiques de l'IHÉS, 137: 107–243, arXiv:2001.04511, doi:10.1007/s10240-023-00139-1. Ravenel, Douglas C. (2003), Complex cobordism and stable homotopy groups of spheres (2nd ed.), AMS Chelsea, ISBN 978-0-8218-2967-7, MR 0860042.

handle.net

hdl.handle.net

Nishida 1973. Nishida, Goro (1973), "The nilpotency of elements of the stable homotopy groups of spheres", Journal of the Mathematical Society of Japan, 25 (4): 707–732, doi:10.2969/jmsj/02540707, hdl:2433/220059, ISSN 0025-5645, MR 0341485.

homotopytypetheory.org

See, e.g., Homotopy type theory 2013, Section 8.1, " ${\textstyle \pi _{1}(S^{1})}$ ". Homotopy type theory—univalent foundations of mathematics, The Univalent Foundations Program and Institute for Advanced Study, 2013, MR 3204653

jstor.org

Serre 1951. Serre, Jean-Pierre (1951), "Homologie singulière des espaces fibrés. Applications", Annals of Mathematics, Second Series, 54 (3): 425–505, doi:10.2307/1969485, JSTOR 1969485, MR 0045386.
Cohen, Moore & Neisendorfer 1979. Cohen, Frederick R.; Moore, John C.; Neisendorfer, Joseph A. (November 1979), "The double suspension and exponents of the homotopy groups of spheres", Annals of Mathematics, Second Series, 110 (3): 549–565, doi:10.2307/1971238, JSTOR 1971238, MR 0554384.
Cohen 1968. Cohen, Joel M. (1968), "The decomposition of stable homotopy", Annals of Mathematics, Second Series, 87 (2): 305–320, doi:10.2307/1970586, JSTOR 1970586, MR 0231377, PMC 224450, PMID 16591550.
Kervaire & Milnor 1963. Kervaire, Michel A.; Milnor, John W. (1963), "Groups of homotopy spheres: I", Annals of Mathematics, 77 (3): 504–537, doi:10.2307/1970128, JSTOR 1970128, MR 0148075.

nih.gov

ncbi.nlm.nih.gov

Cohen 1968. Cohen, Joel M. (1968), "The decomposition of stable homotopy", Annals of Mathematics, Second Series, 87 (2): 305–320, doi:10.2307/1970586, JSTOR 1970586, MR 0231377, PMC 224450, PMID 16591550.

pubmed.ncbi.nlm.nih.gov

Cohen 1968. Cohen, Joel M. (1968), "The decomposition of stable homotopy", Annals of Mathematics, Second Series, 87 (2): 305–320, doi:10.2307/1970586, JSTOR 1970586, MR 0231377, PMC 224450, PMID 16591550.

nus.edu.sg

math.nus.edu.sg

Berrick et al. 2006. Berrick, A. J.; Cohen, Frederick R.; Wong, Yan Loi; Wu, Jie (2006), "Configurations, braids, and homotopy groups", Journal of the American Mathematical Society, 19 (2): 265–326, doi:10.1090/S0894-0347-05-00507-2, MR 2188127.
These tables are based on the table of homotopy groups of spheres in Toda (1962). Toda, Hirosi (1962), Composition methods in homotopy groups of spheres, Annals of Mathematics Studies, vol. 49, Princeton University Press, ISBN 978-0-691-09586-8, MR 0143217 {{citation}}: ISBN / Date incompatibility (help).

projecteuclid.org

Deitmar 2006. Deitmar, Anton (2006), "Remarks on zeta functions and K-theory over F₁", Proceedings of the Japan Academy, Series A, Mathematical Sciences, 82 (8): 141–146, arXiv:math/0605429, doi:10.3792/pjaa.82.141, ISSN 0386-2194, MR 2279281.

psu.edu

citeseerx.ist.psu.edu

Barratt, Jones & Mahowald 1984. Barratt, Michael G.; Jones, John D. S.; Mahowald, Mark E. (1984), "Relations amongst Toda brackets and the Kervaire invariant in dimension 62", Journal of the London Mathematical Society, 30 (3): 533–550, CiteSeerX 10.1.1.212.1163, doi:10.1112/jlms/s2-30.3.533, MR 0810962.

purdue.edu

hopf.math.purdue.edu

May 1999a. May, J. Peter (1999a), "Stable Algebraic Topology 1945–1966", in I. M. James (ed.), History of Topology, Elsevier Science, pp. 665–723, ISBN 978-0-444-82375-5.

rochester.edu

math.rochester.edu

Ravenel 2003, p. 4. Ravenel, Douglas C. (2003), Complex cobordism and stable homotopy groups of spheres (2nd ed.), AMS Chelsea, ISBN 978-0-8218-2967-7, MR 0860042.
Ravenel 2003, p. 25. Ravenel, Douglas C. (2003), Complex cobordism and stable homotopy groups of spheres (2nd ed.), AMS Chelsea, ISBN 978-0-8218-2967-7, MR 0860042.
Ravenel 2003. Ravenel, Douglas C. (2003), Complex cobordism and stable homotopy groups of spheres (2nd ed.), AMS Chelsea, ISBN 978-0-8218-2967-7, MR 0860042.
Ravenel 2003, pp. 67–74. Ravenel, Douglas C. (2003), Complex cobordism and stable homotopy groups of spheres (2nd ed.), AMS Chelsea, ISBN 978-0-8218-2967-7, MR 0860042.
Ravenel 2003, Chapter 5. Ravenel, Douglas C. (2003), Complex cobordism and stable homotopy groups of spheres (2nd ed.), AMS Chelsea, ISBN 978-0-8218-2967-7, MR 0860042.
Fuks 2001. The 2-components can be found in Isaksen, Wang & Xu (2023), and the 3- and 5-components in Ravenel (2003). Fuks, Dmitry B. (2001) [1994], "Spheres, homotopy groups of the", Encyclopedia of Mathematics, EMS Press. Isaksen, Daniel C.; Wang, Guozhen; Xu, Zhouli (2023), "Stable homotopy groups of spheres: from dimension 0 to 90", Publications mathématiques de l'IHÉS, 137: 107–243, arXiv:2001.04511, doi:10.1007/s10240-023-00139-1. Ravenel, Douglas C. (2003), Complex cobordism and stable homotopy groups of spheres (2nd ed.), AMS Chelsea, ISBN 978-0-8218-2967-7, MR 0860042.

semanticscholar.org

api.semanticscholar.org

Hopf 1931. Hopf, Heinz (1931), "Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche", Mathematische Annalen, 104 (1): 637–665, doi:10.1007/BF01457962, S2CID 123533891.
Wang & Xu 2017. Wang, Guozhen; Xu, Zhouli (2017), "The triviality of the 61-stem in the stable homotopy groups of spheres", Annals of Mathematics, 186 (2): 501–580, arXiv:1601.02184, doi:10.4007/annals.2017.186.2.3, MR 3702672, S2CID 119147703.
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st-andrews.ac.uk

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uni-goettingen.de

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worldcat.org

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