Twierdzenie Atiyaha-Singera o indeksie i jego okolicach

• Autorzy: Żoładek H.
• Języki publikacji: PL

Słowa kluczowe

PL

twierdzenie o indeksie; kohomologie snopów; klasy charakterystyczne wiązek

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Roczniki Polskiego Towarzystwa Matematycznego. Seria 2: Wiadomości Matematyczne
• Rocznik: 2005
• Tom: [Z] 41
• Strony: 1--43
• Opis fizyczny: bibliogr. 47 poz.

Twórcy

autor

Żoładek H.

• Warszawa

Bibliografia

• [1] L. Alvarez-Gaumé, Supersymmetry and the Atiyah-Siger index theorem, Commun. Math. Phys. 90 (1983), 161-173.
• [2] M. Atiyah, “Collected works”, v. 1-5, Clarendon Press, Oxford, 1988.
• [3] M. Atiyah, “Geometry of Yang-Mills fields”, Scuola Normale Superiore, Pisa; [również w: “Geometria i fizika uzlov”, Mir, Moskwa, 1995, 79-185].
• [4] M. Atiyah, Anomalies and index theory, Lect. Notes in Phys. 288, Springer- Verlag, New York, 313-322.
• [5] M. Atiyah, Topological aspects of anomalies, w: “Symposium on Anomalies, Geometry and Topology”, World Sci. Press, 1984, 22-32.
• [6] M. Atiyah, Circular symmetry and stationary-phase approximation, w: “Colloquium in honour of Laurent Schwartz”, tom II, Asterisque, 1985, 43-60.
• [7] M. Atiyah, “Geometry and physics of knots”, Cambridge University Press, Cambridge, 1990; [po rosyjsku: Mir, Moskwa, 1995].
• [8] M. Atiyah, R. Bott, A Lefschetz fixed point formula for elliptic differential opearators, Bull. Amer. Math. Soc. 72 (1966), 245-250.
• [9] M. Atiyah, R. Bott, A Lefschetz fixed point formula for elliptic complexes. I, Ann. Math. 86 (1967), 374-407; II. Applications, Ann. Math. 88 (1968), 451-491.
• [10] M. Atiyah, R. Bott, V. K. Patodi, On the heat equation and the index theorem, Invent. Math. 19 (1973), 279-330; Errata to the paper “On the heat equation and the index theorem", Invent. Math. 28 (1975), 277-280.
• [11] M. Atiyah, R. Bott, A. Shapiro, Clifford modules, Topology 3 (1964), 3-38.
• [12] M. Atiyah, H. Donnelly, I. M. Singer, Eta invariant, signature defects and values of L-functions, Ann. Math. 118 (1983), 131-177; Eta invariant, signature defects and values of L-functions: the nonsplit case, Ann. Math. 119 (1984), 635-637.
• [13] M. Atiyah, N. J. Hitchin, V. G. Drinfeld, Y. I. Manin, Construction of instantons, Phys. Letters A65 (1978), 185-187.
• [14] M. Atiyah, N. J. Hitchin, I. M. Singer, Self-duality in four-dimensional geometry, Proc. Roy. Soc. London Ser. A 362 (1978), 425-461.
• [15] M. Atiyah, V. K. Patodi, I. M. Singer, Spectral asymetry and Riemannian geometry, Bull. London Math. Soc. 5 (1973), 229-234.
• [16] M. Atiyah, V. K. Patodi, I. M. Singer, Spectral asymetry and Riemannian geometry. I, Math. Proc. Cambridge Phil. Soc. 77 (1975), 43-69; II, Math. Proc. Cambridge Phil. Soc. 78 (1975), 405-432; III, Math. Proc. Cambridge Phil. Soc. 79 (1976), 71-99.
• [17] M. Atiyah, G. Segal, The index of elliptic operators. II, Ann. Math. 87 (1968), 531-545.
• [18] M. Atiyah, I. M. Singer, The index of elliptic operators on compact manifolds, Bull. Amer. Math. Soc. 69 (1963), 422-433.
• [19] M. Atiyah, I. M. Singer, The index of elliptic operators. I, Ann. Math. 87 (1968), 484-530; III, Ann. Math. 87 (1968), 546-604; IV, Ann. Math. 93 (1971), 119-138; V, Ann. Math. 93 (1971), 139-149.
• [20] M. Atiyah, I. M. Singer, Dirac operators coupled to vector potentials, Proc. Natl. Acad. Sci. USA 8 (1984), 2597-2600.
• [21] M. Atiyah, R. S. Ward, Instantons and algebraic geometry, Comm. Math. Phys. 55 (1977), 117-124.
• [22] W. Barth, K. Hulek, Monads and moduli of vector bundles, Manuscr. Math. 25 (1978), 323-347.
• [23] A. Belavin, A. Polyakov, A. Schwartz, Y. Tyupkin, Pseudo-particle solutions of the Yang-Mills equations, Phys. Letters B59 (1975), 85.
• [24] J.-M. Bismut, The Atiyah-Singer theorems: a probabilistic approach. I. The index theorem, J. Funct. Anal. 57 (1984), 56-99; II. The Lefschetz fixed point formula, J. Funct. Anal. 57 (1984), 320-348.
• [25] J. Cheeger, Analytic torsion and the heat equation, Ann. Math. 109 (1979), 259-322.
• [26] B. A. Dubrovin, S. P. Novikov, A. T. Fomenko, “Modern geometry — methods and applications. III. Introduction to homology theory”, Springer-Verlag, New York, 1990; [po rosyjsku: “Sovremennaja geometria. Metody teorii gomologii”, Nauka, Moskwa, 1984].
• [27] J. J. Duistermaat, G. J. Heckman, On the variation of the cohomology of the symplectic form of the reduced phase space, Invent. Math. 69 (1982), 259- 268; Addendum to “On the variation of the cohomology of the symplectic form of the reduced phase space”, Invent. Math. 72 (1983), 153-158.
• [28] I. M. Gelfand, O elipticeskikh uravneniakh, Uspekhi Mat. Nauk 15 (1960) No 3, 121-132; [po angielsku: Russ. Math. Surv. 15 (1960) No 3, 113].
• [29] E. Getzler, Pseudo-differential operators on supermanifolds and the Atiyah-Singer index theorem, Commun. Math. Phys. 92 (1983), 163-178.
• [30] P. B. Gilkey, “The index theorem and the heat equation”, Publish or Perish Inc., Boston, 1974.
• [31] P. Griffiths, J. Harris, “Principles of algebraic geometry”, John Wiley and Sons, New York, 1978; [po rosyjsku: Mir, Moskwa, 1982].
• [32] F. Hirzebruch, “Topological methods in algebraic geometry”, Springer-Verlag, New York, 1966; [po rosyjsku: Mir, Moskwa, 1973].
• [33] G. Horrocks, Vector bundles on the punctured spectrum of a local ring, Proc. London Math. Soc. 14 (1964), 684-713.
• [34] H. B. Lawson, M.-L. Michelsohn, “Spin geometry”, Princeton Un-ty Press, Princeton, 1989.
• [35] Y. I. Manin, “Gauge field theory and complex geometry”, Springer-Verlag, Berlin, 1997; [po rosyjsku: Nauka, Moskwa, 1984].
• [36] J. Milnor, J. Stasheff, “Characteristic classes”, Ann. Math. Studies 76, Princeton Un-ty Press, Princeton, 1974; [po rosyjsku: Mir, Moskwa 1979].
• [37] “Monopoli. Topologiceskie i variacionnye metody” (pod redakciej M. I. Monastyrskogo i A. G. Sergeeva), Mir, Moskwa, 1989 [po rosyjsku].
• [38] W. Müller, Analytic torsion and R-torsion of Riemannian manifolds, Adv. Math. 28 (1978), 233-305.
• [39] R. S. Palais, “Seminar on the Atiyah-Singer index theorem”, Princeton Un-ty Press, Princeton, 1965; [po rosyjsku: Mir, Moskwa, 1970].
• [40] A. Pressley, G. Segal, “Loop spaces”, Clarendon Press, Oxford, 1986; [po rosyjsku: Mir, Moskwa, 1990].
• [41] D. B. Ray, I. M. Singer, R-torsion and the laplacian on Riemannian manifolds, Adv. Math. 7 (1971), 145-210.
• [42] D. B. Ray, I. M. Singer, Analytic torsion for complex manifolds, Ann. Math. 98 (1973), 154-177.
• [43] M. Raussen, Ch. Skau (interviewers), Interview with Michael Atiyah and Isadore Singer, Europ. Math. Soc. 53 (2004), 24-30.
• [44] R. Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 27 (1953), 198-232.
• [45] E Witten, Quantum field theory and the Jones polynomial, Commun Math Phvs. 117 (1989), 251-399.
• [46] E Witten, Index of elliptic operators, w: “Quantum fields and strings. A course for mathematicians”, tom I (P. Deligne and others, eds.), Amer. Math. Soc, Providence 1999, str. 475-511.
• [47] H. Żołądek, Piąty problem milenijny: istnienie pola Yanga-Millsa i luka masowa, Wiad. Matem. XL (2004), 23-34.