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Equivariant Euler Operators and Characteristics
by
Jonathan Rosenberg
University of Maryland
Coauthors: Wolfgang Lück (Münster)
The Euler characteristic of a compact manifold can be computed analytically in two different ways: by counting (with appropriate signs) the zeros of a "generic" vector field, and by taking the index of the "Euler characteristic operator" d + d* (acting on differential forms, graded by parity of the degree). We discuss the "correct" analogues of these calculations in the situation of a (possibly non-compact) manifold with a proper cocompact action of a discrete group. In particular we answer the question of what information is encoded in the equivariant K-homology class of the Euler characteristic operator.
Date received: April 30, 2003
Copyright © 2003 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # calc-08.