Infinite product decomposition of orbifold mapping spaces

Tamanoi, Hirotaka

doi:10.2140/agt.2009.9.569

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Infinite product decomposition of orbifold mapping spaces

Hirotaka Tamanoi

Algebraic & Geometric Topology 9 (2009) 569–592

DOI: 10.2140/agt.2009.9.569

Abstract

Physicists showed that the generating function of orbifold elliptic genera of symmetric orbifolds can be written as an infinite product. We show that there exists a geometric factorization on space level behind this infinite product formula, and we do this in the much more general framework of orbifold mapping spaces, where factors in the infinite product correspond to finite connected coverings of domain spaces whose fundamental groups are not necessarily abelian. From this formula, a concept of geometric Hecke operators for functors emerges. This is a nonabelian geometric generalization of the usual Hecke operators. We show that these generalized Hecke operators indeed satisfy the identity of the usual Hecke operators for the case of $2$ –dimensional tori.

Keywords

Hecke operators, orbifold elliptic genus, orbifold Euler characteristic, orbifold mapping space, orbifold loop space, symmetric orbifold, wreath product orbifold

Mathematical Subject Classification 2000

Primary: 55N20, 55N91

References

Publication

Received: 1 July 2008

Revised: 20 February 2009

Accepted: 26 February 2009

Published: 30 March 2009

Authors

Hirotaka Tamanoi
Department of Mathematics University of California Santa Cruz 1156 High Street Santa Cruz, CA 95064 United States

Volume 9, issue 1 (2009)