Generalized Orbifold Euler Characteristic of Symmetric Products and Equivariant Morava K-Theory

Details Generalized Orbifold Euler Characteristic of Symmetric Products and Equivariant Morava K-Theory Generalized Orbifold Euler Characteristic of Symmetric Products and Equivariant Morava K-Theory

2001-03-27

arxiv.org/abs/math/0103177v1

Algebraic and Geometric Topology 1 (2001) 115-141

Mathematics

Algebraic Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-6.abs.html

Scientific paper

We introduce the notion of generalized orbifold Euler characteristic associated to an arbitrary group, and study its properties. We then calculate generating functions of higher order (p-primary) orbifold Euler characteristic of symmetric products of a G-manifold M. As a corollary, we obtain a formula for the number of conjugacy classes of d-tuples of mutually commuting elements (of order powers of p) in the wreath product G wreath S_n in terms of corresponding numbers of G. As a topological application, we present generating functions of Euler characteristic of equivariant Morava K-theories of symmetric products of a G-manifold M.

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