The coarse geometry of the Kakimizu complex

Johnson, Jesse; Pelayo, Roberto; Wilson, Robin

doi:10.2140/agt.2014.14.2549

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The coarse geometry of the Kakimizu complex

Jesse Johnson, Roberto Pelayo and Robin Wilson

Algebraic & Geometric Topology 14 (2014) 2549–2560

DOI: 10.2140/agt.2014.14.2549

Abstract

We show that the Kakimizu complex of minimal genus Seifert surfaces for a knot in the $3$ –sphere is quasi-isometric to a Euclidean integer lattice $ℤ^{n}$ for some $n \geq 0$ .

Keywords

Kakimizu complex, Seifert surface, knot theory

Mathematical Subject Classification 2010

Primary: 57M25

Secondary: 57N10

References

Publication

Received: 6 April 2012

Revised: 31 January 2014

Accepted: 7 February 2014

Published: 5 November 2014

Authors

Jesse Johnson
Department of Mathematics Oklahoma State University Stillwater, OK 74078 USA

Roberto Pelayo
Department of Mathematics University of Hawaii at Hilo Hilo, HI 96720 USA

Robin Wilson
Department of Mathematics and Statistics California State Polytechnic University Pomona, CA 91768 USA

Volume 14, issue 5 (2014)