Volume 1, issue 1 (2001)

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Generalized orbifold Euler characteristic of symmetric products and equivariant Morava K–theory

Hirotaka Tamanoi

Algebraic & Geometric Topology 1 (2001) 115–141
 arXiv: math.AT/0103177
Abstract

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 $G\wr {\mathfrak{S}}_{n}$ 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 $M$.

Keywords
equivariant Morava K-theory, generating functions, $G$-sets, Möbius functions, orbifold Euler characteristics, q-series, second quantized manifolds, symmetric products, twisted iterated free loop space, twisted mapping space, wreath products, Riemann zeta function
Mathematical Subject Classification 2000
Primary: 55N20, 55N91
Secondary: 57S17, 57D15, 20E22, 37F20, 05A15
Publication
Revised: 16 February 2001
Accepted: 16 February 2001
Published: 24 February 2001
Authors
 Hirotaka Tamanoi Department of Mathematics University of California Santa Cruz Santa Cruz CA 95064 USA