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

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 2000

Primary: 55N20, 55N91

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

References

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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

Volume 1, issue 1 (2001)

Hirotaka Tamanoi