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

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dc.creatorAlexeevski, A. V.
dc.creatorNatanzon, S. M.
dc.date2007-09-22
dc.date.accessioned2026-07-07T08:31:43Z
dc.date.available2026-07-07T08:31:43Z
dc.descriptionAnalogue 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.
dc.description23 pages
dc.identifierhttps://arxiv.org/abs/0709.3601
dc.identifierhttp://arxiv.org/abs/0709.3601
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/138581
dc.subjectGeometric Topology
dc.subjectRings and Algebras
dc.subject57 M, 16 W
dc.titleHurwitz numbers for regular coverings of surfaces by seamed surfaces and Cardy-Frobenius algebras of finite groups
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