Algebraic & Geometric Topology 1 (2001) 115–141

DOI: 10.2140/agt.2001.1.115

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 ≀ 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

Primary: 55N20, 55N91

Secondary: 05A15, 20E22, 37F20, 57D15, 57S17

References

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Publication

Received: 29 October 2000
Revised: 16 February 2001
Accepted: 16 February 2001
Published: 24 February 2001

Authors