Amphicheiral links with special properties, I
Teruhisa Kadokami
TL;DR
This paper investigates the properties of Alexander polynomials in algebraically split amphicheiral links, proposing a conjecture that such links with an even number of components have zero Alexander polynomial, supported by necessary conditions and examples.
Contribution
It introduces necessary conditions for Alexander polynomials of certain amphicheiral links and proposes a new conjecture regarding their vanishing for links with even components.
Findings
Necessary conditions for Alexander polynomials of amphicheiral links.
Support for the conjecture that such links with even components have zero Alexander polynomial.
Examples illustrating the conditions and conjecture.
Abstract
We provide necessary conditions for the Alexander polynomials of algebraically split component-preservingly amphicheiral links. We raise a conjecture that the Alexander polynomial of an algebraically split component-preservingly amphicheiral link with even components is zero. Our necessary conditions and some examples support the conjecture.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Advanced Algebra and Geometry