On discrete symmetries of the cube of smoothings
Eva Horvat
TL;DR
This paper explores the symmetries of the cube of resolutions in Khovanov homology for links, introducing new combinatorial methods and potential group-theoretic invariants.
Contribution
It identifies symmetries preserving the cube of resolutions and studies their quotient, providing novel combinatorial approaches to compute Khovanov homology.
Findings
Characterization of symmetries of the cube of resolutions
Development of new combinatorial computation methods for Khovanov homology
Potential for new group-theoretic invariants of links
Abstract
We study the Khovanov complex of closed piecewise linear curves in the 3-space. A polygonal link representation endows the cube of resolutions with an additional combinatorial structure. The set of symmetries preserving this structure and its quotient under link equivalence are studied. Our results offer new combinatorial ways of computing Khovanov homology and might lead to other group-theoretic invariants of links.
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Taxonomy
TopicsGeometric and Algebraic Topology · Topological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology