Twistings and the Alexander polynomial

Daren Chen

Twistings and the Alexander polynomial

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arxiv 2202.12489 v1 pith:QSDFIHKO submitted 2022-02-25 math.GT math.QA

Daren Chen This is my paper · ORCID

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keywords alexanderaddingfullpolynomialtwistsobtainedpolynomialsarbitrary

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abstract

We give an explicit formula of the Alexander polynomial of the link obtained by adding an arbitrary number of full twists to positively oriented parallel n-strands in terms of the Alexander polynomials of the links obtained by adding 0,1,...,n-1 full twists. From this, we see that the Alexander polynomials stabilize after adding sufficiently many full twists. The main tool used in the computation is expressing the Alexander polynomial using the vector space representation of $U_{q}(gl(1|1))$.

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Holonomicity from a Heegaard-Floer Perspective
math.GT 2025-01 reject novelty 6.0 of 10

The paper builds S^r-colored knot Floer homology and claims homological q-holonomicity, but the defining notion is vacuous, making the main theorem a tautology.

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