Slice and Gordian numbers of track knots

Details Slice and Gordian numbers of track knots Slice and Gordian numbers of track knots

2005-04-29

arxiv.org/abs/math/0504594v1

Osaka J. Math. 42 (2005), 257-271

Mathematics

Geometric Topology

16 pages, 17 figures

Scientific paper

We present a class of knots associated with labelled generic immersions of intervals into the plane and compute their Gordian numbers and 4-dimensional invariants. At least 10% of the knots in Rolfsen's table belong to this class of knots. We call them track knots. They are contained in the class of quasipositive knots. In this connection, we classify quasipositive knots and strongly quasipositive knots up to 10 crossings.

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