The GSignature Theorem Revisited
Abstract
In a strengthening of the GSignature Theorem of Atiyah and Singer, we compute, at least in principle (modulo certain torsion of exponent dividing a power of the order of G), the class in equivariant Khomology of the signature operator on a Gmanifold, localized at a prime idea of R(G), in terms of the classes in nonequivariant Khomology of the signature operators on fixed sets. The main innovations are that the calculation takes (at least some) torsion into account, and that we are able to extend the calculation to some nonsmooth actions.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 1998
 DOI:
 10.48550/arXiv.math/9812129
 arXiv:
 arXiv:math/9812129
 Bibcode:
 1998math.....12129R
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  KTheory and Homology;
 Mathematics  Operator Algebras;
 58G12 (Primary) 19K33;
 19K35;
 19K56;
 19L47;
 57R91;
 57S17;
 57R85 (Secondary)
 EPrint:
 14 pages, to be published in Proc. International Workshop on Topology, M. Farber, W. Lueck, and S. Weinberger, editors, Contemporary Mathematics, Amer. Math. Soc. The volume is dedicated to Mel Rothenberg