قضیه اندیس عطیه-سینگر (Persian Wikipedia)

Analysis of information sources in references of the Wikipedia article "قضیه اندیس عطیه-سینگر" in Persian language version.

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alainconnes.org

Connes & Moscovici 1990. Connes, A.; Moscovici, H. (1990), "Cyclic cohomology, the Novikov conjecture and hyperbolic groups" (PDF), Topology, 29 (3): 345–388, doi:10.1016/0040-9383(90)90003-3, Zbl 0759.58047, archived from the original (PDF) on 15 December 2020, retrieved 9 June 2021

ams.org

Atiyah, Bott & Patodi 1973. Atiyah, M.; Bott, R.; Patodi, V. K. (1973), "On the heat equation and the index theorem", Invent. Math., 19 (4): 279–330, Bibcode:1973InMat..19..279A, doi:10.1007/BF01425417, MR 0650828, S2CID 115700319. Atiyah, M.; Bott, R.; Patodi, V. K. (1975), "Errata", Invent. Math., 28 (3): 277–280, Bibcode:1975InMat..28..277A, doi:10.1007/BF01425562, MR 0650829
Witten 1982. Witten, Edward (1982), "Supersymmetry and Morse theory", J. Diff. Geom., 17 (4): 661–692, doi:10.4310/jdg/1214437492, MR 0683171

arxiv.org

Hamilton 2020, p. 11. Hamilton, M. J. D. (2020). "The Higgs boson for mathematicians. Lecture notes on gauge theory and symmetry breaking". arXiv:1512.02632 [math.DG].

books.google.com

Palais 1965. Palais, Richard S. (1965), Seminar on the Atiyah–Singer Index Theorem, Annals of Mathematics Studies, vol. 57, S.l.: Princeton Univ Press, ISBN 978-0-691-08031-4 This describes the original proof of the theorem (Atiyah and Singer never published their original proof themselves, but only improved versions of it.)

doi.org

Atiyah & Singer 1963. Atiyah, Michael F.; Singer, Isadore M. (1963), "The Index of Elliptic Operators on Compact Manifolds", Bull. Amer. Math. Soc., 69 (3): 422–433, doi:10.1090/S0002-9904-1963-10957-X An announcement of the index theorem.
Gel'fand 1960. Gel'fand, I. M. (1960), "On elliptic equations", Russ. Math. Surv., 15 (3): 113–123, Bibcode:1960RuMaS..15..113G, doi:10.1070/rm1960v015n03ABEH004094 reprinted in volume 1 of his collected works, p. 65–75, شابک ‎۰−۳۸۷−۱۳۶۱۹−۳. On page 120 Gel'fand suggests that the index of an elliptic operator should be expressible in terms of topological data.
Atiyah & Singer 1968a. Atiyah, Michael F.; Singer, Isadore M. (1968a), "The Index of Elliptic Operators I", Annals of Mathematics, 87 (3): 484–530, doi:10.2307/1970715, JSTOR 1970715 This gives a proof using K-theory instead of cohomology.
Atiyah و Singer (1968a); Atiyah و Singer (1968b); Atiyah و Singer (1971a); Atiyah و Singer (1971b). Atiyah, Michael F.; Singer, Isadore M. (1968a), "The Index of Elliptic Operators I", Annals of Mathematics, 87 (3): 484–530, doi:10.2307/1970715, JSTOR 1970715 This gives a proof using K-theory instead of cohomology. Atiyah, Michael F.; Singer, Isadore M. (1968b), "The Index of Elliptic Operators III", Annals of Mathematics, Second Series, 87 (3): 546–604, doi:10.2307/1970717, JSTOR 1970717 This paper shows how to convert from the K-theory version to a version using cohomology. Atiyah, Michael F.; Singer, Isadore M. (1971a), "The Index of Elliptic Operators IV", Annals of Mathematics, Second Series, 93 (1): 119–138, doi:10.2307/1970756, JSTOR 1970756 This paper studies families of elliptic operators, where the index is now an element of the K-theory of the space parametrizing the family. Atiyah, Michael F.; Singer, Isadore M. (1971b), "The Index of Elliptic Operators V", Annals of Mathematics, Second Series, 93 (1): 139–149, doi:10.2307/1970757, JSTOR 1970757. This studies families of real (rather than complex) elliptic operators, when one can sometimes squeeze out a little extra information.
Kirby & Siebenmann 1969. Kirby, R.; Siebenmann, L.C. (1969), "On the triangulation of manifolds and the Hauptvermutung", Bull. Amer. Math. Soc., 75 (4): 742–749, doi:10.1090/S0002-9904-1969-12271-8
Kasparov 1972. Kasparov, G.G. (1972), "Topological invariance of elliptic operators, I: K-homology", Math. USSR Izvestija (Engl. Transl.), 9 (4): 751–792, Bibcode:1975IzMat...9..751K, doi:10.1070/IM1975v009n04ABEH001497
Atiyah, Bott & Patodi 1973. Atiyah, M.; Bott, R.; Patodi, V. K. (1973), "On the heat equation and the index theorem", Invent. Math., 19 (4): 279–330, Bibcode:1973InMat..19..279A, doi:10.1007/BF01425417, MR 0650828, S2CID 115700319. Atiyah, M.; Bott, R.; Patodi, V. K. (1975), "Errata", Invent. Math., 28 (3): 277–280, Bibcode:1975InMat..28..277A, doi:10.1007/BF01425562, MR 0650829
Witten 1982. Witten, Edward (1982), "Supersymmetry and Morse theory", J. Diff. Geom., 17 (4): 661–692, doi:10.4310/jdg/1214437492, MR 0683171
Teleman 1983. Teleman, N. (1983), "The index of signature operators on Lipschitz manifolds", Publications Mathématiques, 58: 251–290, doi:10.1007/BF02953772, S2CID 121497293, Zbl 0531.58044
Teleman 1984. Teleman, N. (1984), "The index theorem on topological manifolds", Acta Mathematica, 153: 117–152, doi:10.1007/BF02392376, Zbl 0547.58036
Connes 1986. Connes, A. (1986), "Non-commutative differential geometry", Publications Mathématiques, 62: 257–360, doi:10.1007/BF02698807, S2CID 122740195, Zbl 0592.46056
Donaldson & Sullivan 1989. Donaldson, S.K.; Sullivan, D. (1989), "Quasiconformal 4-manifolds", Acta Mathematica, 163: 181–252, doi:10.1007/BF02392736, Zbl 0704.57008
Connes & Moscovici 1990. Connes, A.; Moscovici, H. (1990), "Cyclic cohomology, the Novikov conjecture and hyperbolic groups" (PDF), Topology, 29 (3): 345–388, doi:10.1016/0040-9383(90)90003-3, Zbl 0759.58047, archived from the original (PDF) on 15 December 2020, retrieved 9 June 2021
Connes, Sullivan & Teleman 1994. Connes, A.; Sullivan, D.; Teleman, N. (1994), "Quasiconformal mappings, operators on Hilbert space and local formulae for characteristic classes", Topology, 33 (4): 663–681, doi:10.1016/0040-9383(94)90003-5, Zbl 0840.57013

harvard.edu

ui.adsabs.harvard.edu

Gel'fand 1960. Gel'fand, I. M. (1960), "On elliptic equations", Russ. Math. Surv., 15 (3): 113–123, Bibcode:1960RuMaS..15..113G, doi:10.1070/rm1960v015n03ABEH004094 reprinted in volume 1 of his collected works, p. 65–75, شابک ‎۰−۳۸۷−۱۳۶۱۹−۳. On page 120 Gel'fand suggests that the index of an elliptic operator should be expressible in terms of topological data.
Kasparov 1972. Kasparov, G.G. (1972), "Topological invariance of elliptic operators, I: K-homology", Math. USSR Izvestija (Engl. Transl.), 9 (4): 751–792, Bibcode:1975IzMat...9..751K, doi:10.1070/IM1975v009n04ABEH001497
Atiyah, Bott & Patodi 1973. Atiyah, M.; Bott, R.; Patodi, V. K. (1973), "On the heat equation and the index theorem", Invent. Math., 19 (4): 279–330, Bibcode:1973InMat..19..279A, doi:10.1007/BF01425417, MR 0650828, S2CID 115700319. Atiyah, M.; Bott, R.; Patodi, V. K. (1975), "Errata", Invent. Math., 28 (3): 277–280, Bibcode:1975InMat..28..277A, doi:10.1007/BF01425562, MR 0650829

jstor.org

Atiyah & Singer 1968a. Atiyah, Michael F.; Singer, Isadore M. (1968a), "The Index of Elliptic Operators I", Annals of Mathematics, 87 (3): 484–530, doi:10.2307/1970715, JSTOR 1970715 This gives a proof using K-theory instead of cohomology.
Atiyah و Singer (1968a); Atiyah و Singer (1968b); Atiyah و Singer (1971a); Atiyah و Singer (1971b). Atiyah, Michael F.; Singer, Isadore M. (1968a), "The Index of Elliptic Operators I", Annals of Mathematics, 87 (3): 484–530, doi:10.2307/1970715, JSTOR 1970715 This gives a proof using K-theory instead of cohomology. Atiyah, Michael F.; Singer, Isadore M. (1968b), "The Index of Elliptic Operators III", Annals of Mathematics, Second Series, 87 (3): 546–604, doi:10.2307/1970717, JSTOR 1970717 This paper shows how to convert from the K-theory version to a version using cohomology. Atiyah, Michael F.; Singer, Isadore M. (1971a), "The Index of Elliptic Operators IV", Annals of Mathematics, Second Series, 93 (1): 119–138, doi:10.2307/1970756, JSTOR 1970756 This paper studies families of elliptic operators, where the index is now an element of the K-theory of the space parametrizing the family. Atiyah, Michael F.; Singer, Isadore M. (1971b), "The Index of Elliptic Operators V", Annals of Mathematics, Second Series, 93 (1): 139–149, doi:10.2307/1970757, JSTOR 1970757. This studies families of real (rather than complex) elliptic operators, when one can sometimes squeeze out a little extra information.

mi.ras.ru

Novikov 1965. Novikov, S.P. (1965), "Topological invariance of the rational Pontrjagin classes" (PDF), Doklady Akademii Nauk SSSR, 163: 298–300

mit.edu

www-math.mit.edu

Melrose 1993. Melrose, Richard B. (1993), The Atiyah–Patodi–Singer Index Theorem, Wellesley, Mass.: Peters, ISBN 978-1-56881-002-7 Free online textbook.

numdam.org

Teleman 1983. Teleman, N. (1983), "The index of signature operators on Lipschitz manifolds", Publications Mathématiques, 58: 251–290, doi:10.1007/BF02953772, S2CID 121497293, Zbl 0531.58044
Connes 1986. Connes, A. (1986), "Non-commutative differential geometry", Publications Mathématiques, 62: 257–360, doi:10.1007/BF02698807, S2CID 122740195, Zbl 0592.46056

semanticscholar.org

api.semanticscholar.org

Atiyah, Bott & Patodi 1973. Atiyah, M.; Bott, R.; Patodi, V. K. (1973), "On the heat equation and the index theorem", Invent. Math., 19 (4): 279–330, Bibcode:1973InMat..19..279A, doi:10.1007/BF01425417, MR 0650828, S2CID 115700319. Atiyah, M.; Bott, R.; Patodi, V. K. (1975), "Errata", Invent. Math., 28 (3): 277–280, Bibcode:1975InMat..28..277A, doi:10.1007/BF01425562, MR 0650829
Teleman 1983. Teleman, N. (1983), "The index of signature operators on Lipschitz manifolds", Publications Mathématiques, 58: 251–290, doi:10.1007/BF02953772, S2CID 121497293, Zbl 0531.58044
Connes 1986. Connes, A. (1986), "Non-commutative differential geometry", Publications Mathématiques, 62: 257–360, doi:10.1007/BF02698807, S2CID 122740195, Zbl 0592.46056

web.archive.org

Connes & Moscovici 1990. Connes, A.; Moscovici, H. (1990), "Cyclic cohomology, the Novikov conjecture and hyperbolic groups" (PDF), Topology, 29 (3): 345–388, doi:10.1016/0040-9383(90)90003-3, Zbl 0759.58047, archived from the original (PDF) on 15 December 2020, retrieved 9 June 2021

zbmath.org

Cartan-Schwartz 1965. Cartan-Schwartz (1965), Séminaire Henri Cartan. Théoreme d'Atiyah-Singer sur l'indice d'un opérateur différentiel elliptique. 16 annee: 1963/64 dirigee par Henri Cartan et Laurent Schwartz. Fasc. 1; Fasc. 2. (French), École Normale Supérieure, Secrétariat mathématique, Paris, Zbl 0149.41102
Sullivan 1979. Sullivan, D. (1979), "Hyperbolic geometry and homeomorphisms", J.C. Candrell, "Geometric Topology", Proc. Georgia Topology Conf. Athens, Georgia, 1977, New York: Academic Press, pp. 543–595, ISBN 978-0-12-158860-1, Zbl 0478.57007
Teleman 1983. Teleman, N. (1983), "The index of signature operators on Lipschitz manifolds", Publications Mathématiques, 58: 251–290, doi:10.1007/BF02953772, S2CID 121497293, Zbl 0531.58044
Teleman 1984. Teleman, N. (1984), "The index theorem on topological manifolds", Acta Mathematica, 153: 117–152, doi:10.1007/BF02392376, Zbl 0547.58036
Connes 1986. Connes, A. (1986), "Non-commutative differential geometry", Publications Mathématiques, 62: 257–360, doi:10.1007/BF02698807, S2CID 122740195, Zbl 0592.46056
Donaldson & Sullivan 1989. Donaldson, S.K.; Sullivan, D. (1989), "Quasiconformal 4-manifolds", Acta Mathematica, 163: 181–252, doi:10.1007/BF02392736, Zbl 0704.57008
Connes & Moscovici 1990. Connes, A.; Moscovici, H. (1990), "Cyclic cohomology, the Novikov conjecture and hyperbolic groups" (PDF), Topology, 29 (3): 345–388, doi:10.1016/0040-9383(90)90003-3, Zbl 0759.58047, archived from the original (PDF) on 15 December 2020, retrieved 9 June 2021
Connes, Sullivan & Teleman 1994. Connes, A.; Sullivan, D.; Teleman, N. (1994), "Quasiconformal mappings, operators on Hilbert space and local formulae for characteristic classes", Topology, 33 (4): 663–681, doi:10.1016/0040-9383(94)90003-5, Zbl 0840.57013