Moves relating C-complexes: A correction to Cimasoni's "A geometric construction of the Conway potential function"

Christopher William Davis; Taylor Martin; Carolyn Otto

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arXiv · 2105.10495

Moves relating C-complexes: A correction to Cimasoni's "A geometric construction of the Conway potential function"

Christopher William Davis·Taylor Martin·Carolyn Otto

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Abstract

In groundbreaking work from 2004, Cimasoni gave a geometric computation of the multivariable Conway potential function in terms of a generalization of a Seifert surface for a link called a C-complex. Lemma 3 of that paper provides a family of moves which relates any two C-complexes for a fixed link. This allows for an approach to studying links from the point of view of C-complexes and in following papers it has been used to derive invariants. This lemma is false. We present counterexamples, a correction with detailed proof, and an analysis of the consequences of this error on subsequent works that rely on this lemma.

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BibTeX RIS

Christopher William Davis, Taylor Martin, Carolyn Otto. 2021-05-21. Moves relating C-complexes: A correction to Cimasoni's "A geometric construction of the Conway potential function". https://arxiv.org/abs/2105.10495

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