Open Access
Translator Disclaimer
2009 Infinite product decomposition of orbifold mapping spaces
Hirotaka Tamanoi
Algebr. Geom. Topol. 9(1): 569-592 (2009). DOI: 10.2140/agt.2009.9.569


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.


Download Citation

Hirotaka Tamanoi. "Infinite product decomposition of orbifold mapping spaces." Algebr. Geom. Topol. 9 (1) 569 - 592, 2009.


Received: 1 July 2008; Revised: 20 February 2009; Accepted: 26 February 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1168.55004
MathSciNet: MR2491586
Digital Object Identifier: 10.2140/agt.2009.9.569

Primary: 55N20 , 55N91

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

Rights: Copyright © 2009 Mathematical Sciences Publishers


Vol.9 • No. 1 • 2009
Back to Top