Hurwitz numbers for regular coverings of surfaces by seamed surfaces and Cardy-Frobenius algebras of finite groups

Details Hurwitz numbers for regular coverings of surfaces by seamed surfaces and Cardy-Frobenius algebras of finite groups Hurwitz numbers for regular coverings of surfaces by seamed surfaces and Cardy-Frobenius algebras of finite groups

2007-09-22

arxiv.org/abs/0709.3601v1

Mathematics

Geometric Topology

23 pages

Scientific paper

Analogue of classical Hurwitz numbers is defined in the work for regular coverings of surfaces with marked points by seamed surfaces. Class of surfaces includes surfaces of any genus and orientability, with or without boundaries; coverings may have certain singularities over the boundary and marked points. Seamed surfaces introduced earlier are not actually surfaces. A simple example of seamed surface is book-like seamed surface: several rectangles glued by edges like sheets in a book. We prove that Hurwitz numbers for a class of regular coverings with action of fixed finite group $G$ on cover space such that stabilizers of generic points are conjugated to a fixed subgroup $K\subset G$ defines a new example of Klein Topological Field Theory (KTFT). It is known that KTFTs are in one-to-one correspondence with certain class of algebras, called in the work Cardy-Frobenius algebras. We constructed a wide class of Cardy-Frobenius algebras, including particularly all Hecke algebras for finite groups. Cardy-Frobenius algebras corresponding to regular coverings of surfaces by seamed surfaces are described in terms of group $G$ and its subgroups. As a result, we give an algebraic formula for introduced Hurwitz numbers.

Affiliated with

Also associated with

No associations

Rating

Hurwitz numbers for regular coverings of surfaces by seamed surfaces and Cardy-Frobenius algebras of finite groups 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 Hurwitz numbers for regular coverings of surfaces by seamed surfaces and Cardy-Frobenius algebras of finite groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hurwitz numbers for regular coverings of surfaces by seamed surfaces and Cardy-Frobenius algebras of finite groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-651412