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Equivariant homology

Published online by Cambridge University Press:  24 October 2008

David M. Austin  and
Peter J. Braam
David M. Austin
Affiliation:
Mathematics Department, University of British Columbia, Vancouver BC V6T 1Z2, Canada
Peter J. Braam
Affiliation:
Mathematical Institute, 23–29 St. Giles, Oxford 0X1 3LB
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Abstract

This paper studies the homology of the homotopy quotient of a G-manifold. We start by formulating a complex based on differential forms to compute this homology. This leads to a topological version of integration formulas over fibred products of G-manifolds. In particular the TQFT formulas studied by Witten and Atiyah–Jeffrey now appear as a pairing of homology and cohomology classes. We compare our construction with both the double complex of Axelrod and Witten and with the distributional complex of Duflo and Vergne.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 118 , Issue 1 , July 1995 , pp. 125 - 139
Copyright
Copyright © Cambridge Philosophical Society 1995

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References

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