Teorema del índice de Atiyah-Singer (Spanish Wikipedia)

Analysis of information sources in references of the Wikipedia article "Teorema del índice de Atiyah-Singer" in Spanish language version.

refsWebsite

Global rank Spanish rank

9doi.org

2^nd place

5zentralblatt-math.org

low place

3harvard.edu

18^th place

34^th place

3semanticscholar.org

11^th place

79^th place

3projecteuclid.org

3,707^th place

5,780^th place

2ams.org

451^st place

1,294^th place

1books.google.com

3^rd place

7^th place

1jstor.org

26^th place

56^th place

1mi.ras.ru

low place

1mit.edu

415^th place

495^th place

1numdam.org

8,650^th place

low place

1stackexchange.

low place

ams.org

Atiyah, Bott y 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, MR 0650828, S2CID 115700319, doi:10.1007/BF01425417 .. Atiyah, M.; Bott, R.; Patodi, V. K. (1975), «Errata», Invent. Math. 28 (3): 277-280, Bibcode:1975InMat..28..277A, MR 0650829, doi:10.1007/BF01425562 .
Witten, 1982. Witten, Edward (1982), «Supersymmetry and Morse theory», J. Diff. Geom. 17 (4): 661-692, MR 0683171, doi:10.4310/jdg/1214437492 .

books.google.com

Palais, 1965. Palais, Richard S. (1965), Seminar on the Atiyah–Singer Index Theorem, Annals of Mathematics Studies 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

dx.doi.org

Atiyah y 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, ISBN 0-387-13619-3. On page 120 Gel'fand suggests that the index of an elliptic operator should be expressible in terms of topological data.
Atiyah y Singer, 1968a. Atiyah, Michael F.; Singer, Isadore M. (1968a), «The Index of Elliptic Operators I», Annals of Mathematics 87 (3): 484-530, JSTOR 1970715, doi:10.2307/1970715 . This gives a proof using K-theory instead of cohomology.
Kirby y 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 .
Atiyah, Bott y 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, MR 0650828, S2CID 115700319, doi:10.1007/BF01425417 .. Atiyah, M.; Bott, R.; Patodi, V. K. (1975), «Errata», Invent. Math. 28 (3): 277-280, Bibcode:1975InMat..28..277A, MR 0650829, doi:10.1007/BF01425562 .
Getzler, 1983. Getzler, E. (1983), «Pseudodifferential operators on supermanifolds and the Atiyah–Singer index theorem», Commun. Math. Phys. 92 (2): 163-178, Bibcode:1983CMaPh..92..163G, S2CID 55438589, doi:10.1007/BF01210843 .
Witten, 1982. Witten, Edward (1982), «Supersymmetry and Morse theory», J. Diff. Geom. 17 (4): 661-692, MR 0683171, doi:10.4310/jdg/1214437492 .
Connes, 1986. Connes, A. (1986), «Non-commutative differential geometry», Publications Mathématiques 62: 257-360, S2CID 122740195, Zbl 0592.46056, doi:10.1007/BF02698807 .
Donaldson y Sullivan, 1989. Donaldson, S.K.; Sullivan, D. (1989), «Quasiconformal 4-manifolds», Acta Mathematica 163: 181-252, Zbl 0704.57008, doi:10.1007/BF02392736 .

harvard.edu

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, ISBN 0-387-13619-3. On page 120 Gel'fand suggests that the index of an elliptic operator should be expressible in terms of topological data.
Atiyah, Bott y 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, MR 0650828, S2CID 115700319, doi:10.1007/BF01425417 .. Atiyah, M.; Bott, R.; Patodi, V. K. (1975), «Errata», Invent. Math. 28 (3): 277-280, Bibcode:1975InMat..28..277A, MR 0650829, doi:10.1007/BF01425562 .
Getzler, 1983. Getzler, E. (1983), «Pseudodifferential operators on supermanifolds and the Atiyah–Singer index theorem», Commun. Math. Phys. 92 (2): 163-178, Bibcode:1983CMaPh..92..163G, S2CID 55438589, doi:10.1007/BF01210843 .

jstor.org

Atiyah y Singer, 1968a. Atiyah, Michael F.; Singer, Isadore M. (1968a), «The Index of Elliptic Operators I», Annals of Mathematics 87 (3): 484-530, JSTOR 1970715, doi:10.2307/1970715 . This gives a proof using K-theory instead of cohomology.

mi.ras.ru

Novikov, 1965. Novikov, S.P. (1965), «Topological invariance of the rational Pontrjagin classes», 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

Connes, 1986. Connes, A. (1986), «Non-commutative differential geometry», Publications Mathématiques 62: 257-360, S2CID 122740195, Zbl 0592.46056, doi:10.1007/BF02698807 .

projecteuclid.org

Getzler, 1983. Getzler, E. (1983), «Pseudodifferential operators on supermanifolds and the Atiyah–Singer index theorem», Commun. Math. Phys. 92 (2): 163-178, Bibcode:1983CMaPh..92..163G, S2CID 55438589, doi:10.1007/BF01210843 .
Index Theorems on Open Spaces
Algunos comentarios sobre el documento de Callias

semanticscholar.org

api.semanticscholar.org

Atiyah, Bott y 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, MR 0650828, S2CID 115700319, doi:10.1007/BF01425417 .. Atiyah, M.; Bott, R.; Patodi, V. K. (1975), «Errata», Invent. Math. 28 (3): 277-280, Bibcode:1975InMat..28..277A, MR 0650829, doi:10.1007/BF01425562 .
Getzler, 1983. Getzler, E. (1983), «Pseudodifferential operators on supermanifolds and the Atiyah–Singer index theorem», Commun. Math. Phys. 92 (2): 163-178, Bibcode:1983CMaPh..92..163G, S2CID 55438589, doi:10.1007/BF01210843 .
Connes, 1986. Connes, A. (1986), «Non-commutative differential geometry», Publications Mathématiques 62: 257-360, S2CID 122740195, Zbl 0592.46056, doi:10.1007/BF02698807 .

stackexchange.

math.stackexchange.

com/questions/41182/how-to-understand-the-todd-class «topología algebraica - ¿Cómo entender la clase Todd?». Mathematics Stack Exchange. Consultado el 5 de febrero de 2021.

zentralblatt-math.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 .
Atiyah, 1970. Atiyah, M. F. (1970), «Global Theory of Elliptic Operators», Proc. Int. Conf. on Functional Analysis and Related Topics (Tokyo, 1969), University of Tokio, Zbl 0193.43601 .
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 .
Connes, 1986. Connes, A. (1986), «Non-commutative differential geometry», Publications Mathématiques 62: 257-360, S2CID 122740195, Zbl 0592.46056, doi:10.1007/BF02698807 .
Donaldson y Sullivan, 1989. Donaldson, S.K.; Sullivan, D. (1989), «Quasiconformal 4-manifolds», Acta Mathematica 163: 181-252, Zbl 0704.57008, doi:10.1007/BF02392736 .