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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 Sn 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
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Publication
Received: 29 October 2000
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