Noncommutative two-dimensional topological field theories and Hurwitz numbers for real algebraic curves

• Autores: A. Alexeevski, Sergey M. Natanzon
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 12, Nº. 3-4, 2006, págs. 307-377
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • It is well known that the classical two-dimensional topological field theories are in one-to-one correspondence with the commutative Frobenius algebras. An important extension of classical two-dimensional topological field theories is provided by open-closed two-dimensional topological field theories. In this paper we extend open-closed two-dimensional topological field theories to nonorientable surfaces. We call them Klein topological field theories (KTFT).

    We prove that KTFTs bijectively correspond to (in general noncommutative) algebras with certain additional structures, called structure algebras. The semisimple structure algebras are classified. Starting from an arbitrary finite group, we construct a structure algebra and prove that it is semisimple.

    We define an analog of Hurwitz numbers for real algebraic curves and prove that they are correlators of a KTFT. The structure algebra of this KTFT is the structure algebra of a symmetric group