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.

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Hirotaka Tamanoi
Department of Mathematics, University of California Santa Cruz,
Santa Cruz, CA 95064, USA

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