Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

$ K$-theoretical index theorems for good orbifolds


Author: Carla Farsi
Journal: Proc. Amer. Math. Soc. 115 (1992), 769-773
MSC: Primary 58G10; Secondary 19K56, 46L80, 57R15
MathSciNet review: 1127139
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] Michael Francis Atiyah, Elliptic operators and compact groups, Lecture Notes in Mathematics, Vol. 401, Springer-Verlag, Berlin, 1974. MR 0482866 (58 #2910)
  • [2] M. F. Atiyah, Elliptic operators, discrete groups and von Neumann algebras, Colloque “Analyse et Topologie” en l’Honneur de Henri Cartan (Orsay, 1974), Soc. Math. France, Paris, 1976, pp. 43–72. Astérisque, No. 32-33. MR 0420729 (54 #8741)
  • [3] M. F. Atiyah and I. M. Singer, The index of elliptic operators. III, Ann. of Math. (2) 87 (1968), 546–604. MR 0236952 (38 #5245)
  • [4] J. L. Brylinski, Algebras associated with group actions and their homology, preprint.
  • [5] A. Connes, The Chern character in $ K$-homology, part I, Non commutative differential geometry, Inst. Hautes Études Sci. Publ. Math. 62 (1986), 257-360.
  • [6] Carla Farsi, 𝐾-theoretical index theorems for orbifolds, Quart. J. Math. Oxford Ser. (2) 43 (1992), no. 170, 183–200. MR 1164622 (93f:58231), http://dx.doi.org/10.1093/qmath/43.2.183
  • [7] 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 (84k:58215)
  • [8] 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 (58 #7603)
  • [9] -, An index for invariant elliptic operators, $ K$-theory, and representations of Lie groups, Soviet Math. Dokl. 27 (1983), 105-109.
  • [10] -, 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.
  • [11] Tetsuro Kawasaki, The signature theorem for 𝑉-manifolds, Topology 17 (1978), no. 1, 75–83. MR 0474432 (57 #14072)
  • [12] Tetsuro Kawasaki, The Riemann-Roch theorem for complex 𝑉-manifolds, Osaka J. Math. 16 (1979), no. 1, 151–159. MR 527023 (80f:58042)
  • [13] Tetsuro Kawasaki, The index of elliptic operators over 𝑉-manifolds, Nagoya Math. J. 84 (1981), 135–157. MR 641150 (83i:58095)
  • [14] A. Miščenko and A. T. Fomenko, The index of elliptic operators over $ {C^*}$-algebras, Math. USSR-Izv. 15 (1980), 87-112.
  • [15] Marc A. Rieffel, Applications of strong Morita equivalence to transformation group 𝐶*-algebras, Operator algebras and applications, Part I (Kingston, Ont., 1980) Proc. Sympos. Pure Math., vol. 38, Amer. Math. Soc., Providence, R.I., 1982, pp. 299–310. MR 679709 (84k:46046)
  • [16] Ichirô Satake, The Gauss-Bonnet theorem for 𝑉-manifolds, J. Math. Soc. Japan 9 (1957), 464–492. MR 0095520 (20 #2022)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58G10, 19K56, 46L80, 57R15

Retrieve articles in all journals with MSC: 58G10, 19K56, 46L80, 57R15


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1127139-5
PII: S 0002-9939(1992)1127139-5
Keywords: $ K$-theory, orbifolds, index, Gauss-Bonnet
Article copyright: © Copyright 1992 American Mathematical Society