The behavior of the maximal degree of the Khovanov homology under twisting
Keiji Tagami
TL;DR
This paper investigates how the highest homological degree in Khovanov homology changes when a knot undergoes twisting, providing insights into the algebraic structure of knot invariants.
Contribution
It introduces a detailed analysis of the maximal degree behavior of Khovanov homology under twisting operations, a novel focus in knot theory.
Findings
Maximal degree exhibits predictable patterns under twisting.
Twisting can increase or decrease the maximal degree depending on the knot.
Results contribute to understanding the stability of Khovanov homology features.
Abstract
In this paper, we study the behavior of the maximal homological degree of the non-zero Khovanov homology groups under twisting.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics