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The index of elliptic operators over V-manifolds

Published online by Cambridge University Press:  22 January 2016

Tetsuro Kawasaki
Tetsuro Kawasaki*
Affiliation:
Department of Mathematics Faculty of Science, Gakushuin University, Mejiro, Tokyo, 171, Japan
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Let M be a compact smooth manifold and let G be a finite group acting smoothly on M. Let E and F be smooth G-equivariant complex vector bundles over M and let be a G-invariant elliptic pseudo-differential operator. Then the kernel and the cokernel of the operator P are finite-dimensional representations of G. The difference of the characters of these representations is an element of the representation ring R(G) of G and is called the G-index of the operator P.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 84 , December 1981 , pp. 135 - 157
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1981

References

[ 1 ] Atiyah, M.F., Elliptic operators and compact groups, Lecture Notes in Math., 401, Springer-Verlag, 1974.Google Scholar
[ 2 ] Atiyah, M.F. and Singer, I.M., The index of elliptic operators, I, Ann. of Math., 87 (1968), 484–530.CrossRefGoogle Scholar
[ 3 ] Atiyah, M.F. and Singer, I.M., The index of elliptic operators, III, Ann. of Math., 87 (1968), 546–604.CrossRefGoogle Scholar
[ 4 ] Borel, A. and Hirzebruch, F., Characteristic classes and homogeneous spaces, I, Amer. J. Math., 80 (1958), 458–538.CrossRefGoogle Scholar
[ 5 ] Borel, A. and Hirzebruch, F., Characteristic classes and homogeneous spaces, II, Amer. J. Math., 81 (1959), 315–382.CrossRefGoogle Scholar
[ 6 ] Kawasaki, T., The signature theorem for V-manifolds, Topology, 17 (1978), 75–83.Google Scholar
[ 7 ] Kawasaki, T., The Riemann-Roch theorem for complex V-manifolds, Osaka J. Math., 16 (1979), 151–159.Google Scholar