English

On links with locally infinite {K}akimizu complexes

Geometric Topology 2014-10-01 v2

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 LL only has connected Seifert surfaces and has a locally infinite Kakimizu complex then LL is a satellite of either a torus knot, a cable knot or a connected sum, with winding number 0.

Keywords

Cite

@article{arxiv.1010.3831,
  title  = {On links with locally infinite {K}akimizu complexes},
  author = {Jessica E. Banks},
  journal= {arXiv preprint arXiv:1010.3831},
  year   = {2014}
}

Comments

9 pages, 5 figures; v2 minor has minor changes incorporating referee's comments. To appear in Algebraic & Geometric Topology

R2 v1 2026-06-21T16:30:37.620Z