Orbifold Euler characteristics and the number of commuting n-tuples in symmetric groups
Combinatorics
2007-05-23 v1 Algebraic Topology
Abstract
Generating functions for the number of commuting m-tuples in the symmetric groups are obtained. We define a natural sequence of ``orbifold Euler characteristics'' for a finite group G acting on a manifold X. Our definition generalizes the ordinary Euler characteristic of X/G and the string-theoretic orbifold Euler characteristic. Our formulae for commuting m-tuples underlie formulas that generalize the results of Macdonald and Hirzebruch-Hofer concerning the ordinary and string-theoretic Euler characteristics of symmetric products.
Keywords
Cite
@article{arxiv.math/9712248,
title = {Orbifold Euler characteristics and the number of commuting n-tuples in symmetric groups},
author = {Jim Bryan and Jason Fulman},
journal= {arXiv preprint arXiv:math/9712248},
year = {2007}
}