The quasi-isomorphism class of the Kakimizu complex

TL;DR

This paper investigates the Kakimizu complex of a knot, establishing bounds on its quasi-isomorphism class and providing a precise characterization of its structure.

Contribution

It offers a matching lower bound on the dimension of the Kakimizu complex, complementing previous upper bounds, thus clarifying its quasi-isomorphism class.

Findings

Lower bound on the dimension of the Kakimizu complex

Matching the previously known upper bound

The Kakimizu complex is quasi-isomorphic to ^n for some n

Abstract

It has been shown that the Kakimizu complex of a knot is quasi-isomorphic to $\mathbb{Z}^n$ for some $n \geq 0$. We give a lower bound on $n$, matching the upper bound previously given.