The G-Signature Theorem Revisited

Details The G-Signature Theorem Revisited The G-Signature Theorem Revisited

1998-12-22

arxiv.org/abs/math/9812129v1

Mathematics

Differential Geometry

14 pages, to be published in Proc. International Workshop on Topology, M. Farber, W. Lueck, and S. Weinberger, editors, Contem

Scientific paper

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.

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