A combinatorial proof of invariance of double-point enhanced grid homology
Timothy Ratigan, Joshua Wang, Luya Wang
TL;DR
This paper provides a purely combinatorial proof that the "minus" version of Lipshitz's double-point enhanced grid homology is an invariant of knots, confirming its robustness in knot theory.
Contribution
It introduces a combinatorial proof establishing the invariance of the "minus" version of Lipshitz's double-point enhanced grid homology for knots.
Findings
Confirmed the invariance of the homology under knot isotopies
Provided a combinatorial framework for the proof
Strengthened the theoretical foundation of grid homology
Abstract
We prove that the "minus" version of Lipshitz's double-point enhanced grid homology is a knot invariant through purely combinatorial means.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology