#### Algebraic and Geometric Topology 1 (2001),
paper no. 6, pages 115-141.

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

### Hirotaka Tamanoi

**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 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.
**Keywords**.
Equivariant Morava K-theory, generating functions, G-sets, Moebius
functions, orbifold Euler characteristics, q-series, second quantized
manifolds, symmetric products, twisted iterated free loop space,
twisted mapping space, wreath products, Riemann zeta function

**AMS subject classification**.
Primary: 55N20, 55N91.
Secondary: 57S17, 57D15, 20E22, 37F20, 05A15.

**DOI:** 10.2140/agt.2001.1.115

**E-print:** `arXiv:math.AT/0103177`

Submitted: 29 October 2000.
(Revised: 16 February 2001.)
Accepted: 16 February 2001.
Published: 24 February 2001.

Notes on file formats
Hirotaka Tamanoi

Department of Mathematics, University of California Santa Cruz,

Santa Cruz, CA 95064, USA

Email: tamanoi@math.ucsc.edu

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