Linking forms of amphichiral knots
Stefan Friedl, Allison N. Miller, Mark Powell
TL;DR
This paper introduces a straightforward homological obstruction criterion to determine whether a knot is amphichiral, applicable to both positive and negative cases, by analyzing the 2-fold branched cover.
Contribution
It provides a new, simple obstruction method based on homology for identifying amphichiral knots, expanding previous techniques.
Findings
Obstruction criterion for amphichirality using homology
Applicable to unoriented knots, covering both positive and negative cases
Simplifies detection of amphichiral knots
Abstract
We give a simple obstruction for a knot to be amphichiral, in terms of the homology of the 2-fold branched cover. We work with unoriented knots, and so obstruct both positive and negative amphichirality.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics