Volume 1, issue 1 (2001)

Download this article
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
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


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.

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
Forward citations
Received: 29 October 2000
Revised: 16 February 2001
Accepted: 16 February 2001
Published: 24 February 2001
Hirotaka Tamanoi
Department of Mathematics
University of California Santa Cruz
Santa Cruz CA 95064