Grid homology and the unknotting number
Zipei Zhuang
TL;DR
This paper demonstrates that the order of torsion homology classes in grid homology provides a lower bound for the unknotting number of a knot, linking algebraic invariants to knot complexity.
Contribution
It introduces a novel algebraic approach connecting grid homology torsion classes to unknotting number bounds.
Findings
Torsion homology class order bounds the unknotting number.
Provides a new algebraic method for estimating knot complexity.
Establishes a link between grid homology and classical knot invariants.
Abstract
We showed that the order of torsion homology classes in the grid homology of a knot is a lower bound for the unknotting number.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis