Homotopical Khovanov homology
Vassily Olegovich Manturov, Igor Nikonov
TL;DR
This paper introduces a new homotopical grading to the Khovanov complex, creating a triply graded homological invariant for links in thickened surfaces, enhancing the understanding of link homology.
Contribution
It develops a modified Khovanov complex with a novel homotopical grading for links in thickened surfaces, expanding the framework of link invariants.
Findings
Defines a triply graded homological invariant for links in thickened surfaces.
Incorporates a new homotopical grading into the Khovanov complex.
Provides a refined tool for studying link homology in surface contexts.
Abstract
We modify the definition of the Khovanov complex for oriented links in a thickening of an oriented surface to obtain a triply graded homological link invariant with a new homotopical grading.
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