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2010•Journal of TopologyRequires access

The Kakimizu complex is simply connected

Jennifer Schultens

Open publisher page 8 citations

Abstract

In 1992, Osamu Kakimizu defined a complex that has become known as the Kakimizu complex of a knot. Vertices correspond to isotopy classes of minimal genus Seifert surfaces of the knot. Higher-dimensional simplices correspond to collections of such classes of Seifert surfaces that admit disjoint representatives. We show that this complex is simply connected.

About this research paper

What this paper is about

In 1992, Osamu Kakimizu defined a complex that has become known as the Kakimizu complex of a knot. Vertices correspond to isotopy classes of minimal genus Seifert surfaces of the knot. Higher-dimensional simplices correspond to collections of such classes of Seifert surfaces that admit disjoint representatives. We show that this complex is simply connected.

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OpenAlex reports 8 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In 1992, Osamu Kakimizu defined a complex that has become known as the Kakimizu complex of a knot. Vertices correspond to isotopy classes of minimal genus Seifert surfaces of the knot. Higher-dimensional simplices correspond to collections of such classes of Seifert surfaces that admit disjoint representatives. We show that this complex is simply connected.

Key concepts: Isotopy, Knot (papermaking), Mathematics, Disjoint sets, Combinatorics, Seifert surface, Simply connected space, Genus

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