On links with locally infinite {K}akimizu complexes

Details On links with locally infinite {K}akimizu complexes On links with locally infinite {K}akimizu complexes

2010-10-19

arxiv.org/abs/1010.3831v2

Mathematics

Geometric Topology

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

Scientific paper

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.

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