Generalized orbifold Euler characteristics of symmetric orbifolds and covering spaces

Details Generalized orbifold Euler characteristics of symmetric orbifolds and covering spaces Generalized orbifold Euler characteristics of symmetric orbifolds and covering spaces

2003-09-07

arxiv.org/abs/math/0309133v1

Algebr. Geom. Topol. 3 (2003) 791-856

Mathematics

Group Theory

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-27.abs.html

Scientific paper

Let G be a finite group and let M be a G-manifold. We introduce the concept of generalized orbifold invariants of M/G associated to an arbitrary group Gamma, an arbitrary Gamma-set, and an arbitrary covering space of a connected manifold Sigma whose fundamental group is Gamma. Our orbifold invariants have a natural and simple geometric origin in the context of locally constant G-equivariant maps from G-principal bundles over covering spaces of Sigma to the G-manifold M. We calculate generating functions of orbifold Euler characteristic of symmetric products of orbifolds associated to arbitrary surface groups (orientable or non-orientable, compact or non-compact), in both an exponential form and in an infinite product form. Geometrically, each factor of this infinite product corresponds to an isomorphism class of a connected covering space of a manifold Sigma. The essential ingredient for the calculation is a structure theorem of the centralizer of homomorphisms into wreath products described in terms of automorphism groups of Gamma-equivariant G-principal bundles over finite Gamma-sets. As corollaries, we obtain many identities in combinatorial group theory. As a byproduct, we prove a simple formula which calculates the number of conjugacy classes of subgroups of given index in any group. Our investigation is motivated by orbifold conformal field theory.

Affiliated with

Also associated with

No associations

Rating

Generalized orbifold Euler characteristics of symmetric orbifolds and covering spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Generalized orbifold Euler characteristics of symmetric orbifolds and covering spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized orbifold Euler characteristics of symmetric orbifolds and covering spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-47777