The Kakimizu complex of a split link
Jessica E. Banks
TL;DR
This paper investigates the structure of the Kakimizu complex for split and non-split links, revealing uniqueness properties of simplices and enhancing understanding of Seifert surfaces in these contexts.
Contribution
It introduces new results on the realization and structure of the Kakimizu complex for split and non-split links, including uniqueness of simplices.
Findings
A simplex of the Kakimizu complex of a non-split link can be realized uniquely.
The study extends understanding of Seifert surfaces for split and non-split links.
Provides new insights into the topology of the Kakimizu complex.
Abstract
We study the Kakimizu complex of a split link. As part of this, we also study Seifert surfaces and the Kakimizu complex for a non-split link in a 3-ball. In addition, we show that a simplex of the Kakimizu complex of a non-split link can be realised in an essentially unique way.
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Taxonomy
TopicsGeometric and Algebraic Topology · Topological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology