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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$K$-theoretical index theorems for good orbifolds
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by Carla Farsi
Proc. Amer. Math. Soc. 115 (1992), 769-773
DOI: https://doi.org/10.1090/S0002-9939-1992-1127139-5
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Abstract:

In this note we study index theory for general and good orbifolds. We prove a $K$-theoretical index theorem for good orbifolds, and from this we deduce as a corollary a numerical index formula.
References
  • Michael Francis Atiyah, Elliptic operators and compact groups, Lecture Notes in Mathematics, Vol. 401, Springer-Verlag, Berlin-New York, 1974. MR 0482866
  • M. F. Atiyah, Elliptic operators, discrete groups and von Neumann algebras, Colloque “Analyse et Topologie” en l’Honneur de Henri Cartan (Orsay, 1974) Astérisque, No. 32-33, Soc. Math. France, Paris, 1976, pp. 43–72. MR 0420729
  • M. F. Atiyah and I. M. Singer, The index of elliptic operators. III, Ann. of Math. (2) 87 (1968), 546–604. MR 236952, DOI 10.2307/1970717
    • J. L. Brylinski, Algebras associated with group actions and their homology, preprint. A. Connes, The Chern character in $K$-homology, part I, Non commutative differential geometry, Inst. Hautes Études Sci. Publ. Math. 62 (1986), 257-360.
  • Carla Farsi, $K$-theoretical index theorems for orbifolds, Quart. J. Math. Oxford Ser. (2) 43 (1992), no. 170, 183–200. MR 1164622, DOI 10.1093/qmath/43.2.183
  • Michel Hilsum, Opérateurs de signature sur une variété lipschitzienne et modules de Kasparov non bornés, C. R. Acad. Sci. Paris Sér. I Math. 297 (1983), no. 1, 49–52 (French, with English summary). MR 719945
  • G. G. Kasparov, Topological invariants of elliptic operators. I. $K$-homology, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975), no. 4, 796–838 (Russian); Russian transl., Math. USSR-Izv. 9 (1975), no. 4, 751–792 (1976). MR 0488027
    • —, An index for invariant elliptic operators, $K$-theory, and representations of Lie groups, Soviet Math. Dokl. 27 (1983), 105-109. —, Operator $K$-theory and its applications: elliptic operators, group representations, higher signatures, ${C^*}$-extensions, Proc. Internat. Congr. of Mathematicians, Aug. 16-24, 1983, Warsaw, 1983, pp. 987-1000.
  • Tetsuro Kawasaki, The signature theorem for $V$-manifolds, Topology 17 (1978), no. 1, 75–83. MR 474432, DOI 10.1016/0040-9383(78)90013-7
  • Tetsuro Kawasaki, The Riemann-Roch theorem for complex $V$-manifolds, Osaka Math. J. 16 (1979), no. 1, 151–159. MR 527023
  • Tetsuro Kawasaki, The index of elliptic operators over $V$-manifolds, Nagoya Math. J. 84 (1981), 135–157. MR 641150
    • A. Miščenko and A. T. Fomenko, The index of elliptic operators over ${C^*}$-algebras, Math. USSR-Izv. 15 (1980), 87-112.
  • Marc A. Rieffel, Applications of strong Morita equivalence to transformation group $C^{\ast }$-algebras, Operator algebras and applications, Part 1 (Kingston, Ont., 1980) Proc. Sympos. Pure Math., vol. 38, Amer. Math. Soc., Providence, R.I., 1982, pp. 299–310. MR 679709
  • Ichirô Satake, The Gauss-Bonnet theorem for $V$-manifolds, J. Math. Soc. Japan 9 (1957), 464–492. MR 95520, DOI 10.2969/jmsj/00940464
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Bibliographic Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 115 (1992), 769-773
  • MSC: Primary 58G10; Secondary 19K56, 46L80, 57R15
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1127139-5
  • MathSciNet review: 1127139