The G-Signature Theorem Revisited
Abstract
In a strengthening of the G-Signature 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 K-homology of the signature operator on a G-manifold, localized at a prime idea of R(G), in terms of the classes in non-equivariant K-homology 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 non-smooth actions.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- December 1998
- DOI:
- 10.48550/arXiv.math/9812129
- arXiv:
- arXiv:math/9812129
- Bibcode:
- 1998math.....12129R
- Keywords:
-
- Mathematics - Differential Geometry;
- Mathematics - K-Theory and Homology;
- Mathematics - Operator Algebras;
- 58G12 (Primary) 19K33;
- 19K35;
- 19K56;
- 19L47;
- 57R91;
- 57S17;
- 57R85 (Secondary)
- E-Print:
- 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