Volume 11, issue 3 (2011)

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On links with locally infinite Kakimizu complexes

Jessica E Banks

Algebraic & Geometric Topology 11 (2011) 1445–1454
Abstract

We show that the Kakimizu complex of a knot may be locally infinite, answering a question of Przytycki–Schultens. We then prove that if a link L only has connected Seifert surfaces and has a locally infinite Kakimizu complex then L is a satellite of either a torus knot, a cable knot or a connected sum, with winding number 0.

Keywords
links, Kakimizu complex, Seifert surface
Mathematical Subject Classification 2010
Primary: 57M25
References
Publication
Received: 1 November 2010
Revised: 14 March 2011
Accepted: 30 March 2011
Published: 17 May 2011
Authors
Jessica E Banks
Mathematical Institute
University of Oxford
24–29 St Giles’
Oxford
OX1 3LB
UK