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This paper is devoted to the study of algebraic structures leading to link homology theories. The originally used structures of Frobenius algebra and/or TQFT are modified in two directions. First, we refine 2-dimensional cobordisms by taking into account their embedding into the three space. Secondly, we extend the underlying cobordism category to a 2-category, where the usual relations hold up to 2-isomorphisms. The corresponding abelian 2-functor is called an extended quantum field theory (EQFT). We show that the Khovanov homology, the nested Khovanov homology, extracted by Stroppel and Webster from Seidel-Smith construction, and the odd Khovanov homology fit into this setting. Moreover, we prove that any EQFT based on a Z_2-extension of the embedded cobordism category which coincides with Khovanov after reducing the coefficients modulo 2, gives rise to a link invariant homology theory isomorphic to those of Khovanov.

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Beliakova , Anna -  Wagner , Emmanuel - 

Id.: 71376675

Idioma: inglés  - 

Versión: 1.0

Estado: Final

Palabras clave57R58, 57M27 - 

Tipo de recurso: info:eu-repo/semantics/preprint  -  Preprints, Working Papers, ...  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

Requerimientos técnicos:  Browser: Any - 

Relación: [References] info:eu-repo/semantics/altIdentifier/arxiv/ 0910.5050

Fecha de contribución: 09-jun-2018


* hal-00426628

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