On links with locally infinite Kakimizu complexes

Banks, Jessica E

doi:10.2140/agt.2011.11.1445

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On links with locally infinite Kakimizu complexes

Jessica E Banks

Algebraic & Geometric Topology 11 (2011) 1445–1454

DOI: 10.2140/agt.2011.11.1445

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

Volume 11, issue 3 (2011)