2021/05/21 by Davis, Christopher William, Martin, Taylor, Otto, Carolyn · 2 citations
#57K10 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2105.10495
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.