Khovanov homology and diagonalisable Frobenius algebras
Paul Turner
TL;DR
This paper provides an elementary proof demonstrating that Khovanov-type link homology, when constructed from a diagonalisable Frobenius algebra, results in a degenerate homology, simplifying understanding of its structure.
Contribution
It offers a straightforward proof that Khovanov-type homology from diagonalisable Frobenius algebras is degenerate, clarifying the algebraic conditions leading to trivial homology.
Findings
Khovanov-type homology is degenerate for diagonalisable Frobenius algebras
Elementary proof simplifies previous complex arguments
Clarifies the algebraic conditions for homology degeneracy
Abstract
We give a short elementary proof that a Khovanov-type link homology constructed from a diagonalisable Frobenius algebra is degenerate.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models