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

Primary: 57M25

References

Publication

Received: 1 November 2010
Revised: 14 March 2011
Accepted: 30 March 2011
Published: 17 May 2011

Authors