Please use this identifier to cite or link to this item: http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/7904
Title: Simplicial Complexes on Seifert Surfaces of Links
Authors: Schultens, Jennifer
BEZBARUA, IPSA
Dept. of Mathematics
20181124
Keywords: Cyclic covering space
Simplicial complex
Kakimizu complex
Contractibility
Coarse geometry
Local infiniteness
Issue Date: May-2023
Citation: 115
Abstract: In this thesis project, we study various properties related to two well-known simplicial complexes on the Seifert surfaces of links - the incompressible complex and the Kakimizu complex (named after Osamu Kakimizu). We first look at Kakimizu’s original paper from 1992, in which he defines these complexes and describes a metric coming from the cyclic covering space of the knot complement, which is the same as the graph metric on the complexes. Then we study various properties of the Kakimizu complex, like connectedness, contractibility, local infiniteness and its coarse geometry. Finally, we try to extend some of these properties to the incompressible complex, and find a restriction on the types of knots that can have Kakimizu complex homeomorphic to the real line.
URI: http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/7904
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