The algebra of bipartite graphs and Hurwitz numbers of seamed surfacesстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:A Klein surface is a compact surface endowed with a dianalytic
structure. Klein surfaces may have boundary and may be orientable or
non-orientable surfaces. An orientable Klein surface without boundary is a
Riemann surface. Given some Klein surfaces with boundary, seamed Klein
surfaces can be obtained by gluing them along boundary points. It is
required that the transition functions induced on the boundary be dianalytic
everywhere outside a finite set and that the punctured neighbourhood of any
point be connected. \par In the paper under review morphisms of degree $n$
from seamed surfaces to Klein surfaces are considered. The authors extend
the definition of Hurwitz numbers to seamed surfaces. They study the algebra
of bipartite graphs and Cardy-Frobenius algebras. These algebras are in
one-to-one correspondence with Klein topological field theories, introduced
by the authors in [Sel. Math., New Ser. 12, No. 3--4, 307--377 (2006; Zbl
1158.57304)]. Klein topological field theories are an extension of
open-closed topological field theories to non-orientable surfaces. The
authors describe all Cardy-Frobenius algebras corresponding to Hurwitz
numbers of seamed surfaces and provide an effective method for calculating
them.