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A Proof of the Kashaev Signature Conjecture

Geometric Topology 2023-11-06 v1

Abstract

In 2018 Kashaev introduced a diagrammatic link invariant conjectured to be twice the Levine-Tristram signature. If true, the conjecture would provide a simple way of computing the Levine-Tristram signature of a link by taking the signature of a real symmetric matrix associated with a corresponding link diagram. This paper establishes the conjecture using the Seifert surface definition of the Levine-Tristram signature on the disjoint union of an oriented link and its reverse. The proof also reveals yet another formula for the Alexander polynomial.

Keywords

Cite

@article{arxiv.2311.01923,
  title  = {A Proof of the Kashaev Signature Conjecture},
  author = {Jessica Liu},
  journal= {arXiv preprint arXiv:2311.01923},
  year   = {2023}
}

Comments

11 pages, 9 figures