TL;DR
This paper demonstrates how Khovanov homology, linked to rank 2 Frobenius algebras, can be adapted to define a TQFT on oriented links, establishing a functorial relationship with cobordisms.
Contribution
It introduces a method to modify Khovanov homology to produce a TQFT, connecting link invariants with cobordism categories in a functorial manner.
Findings
Khovanov homology can be functorially related to cobordisms
A construction of TQFT from Khovanov homology is provided
The approach applies to Frobenius algebras of rank 2
Abstract
In this paper we prove that every Khovanov homology associated to a Frobenius algebra of rank can be modified in such a way as to produce a TQFT on oriented links, that is a monoidal functor from the category of cobordisms of oriented links to the homotopy category of complexes.
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