Persistent laminations from Seifert surfaces

Details Persistent laminations from Seifert surfaces Persistent laminations from Seifert surfaces

1998-07-24

arxiv.org/abs/math/9807139v1

Mathematics

Geometric Topology

14 pages, with 15 figures

Scientific paper

A persistent lamination for a knot K is an essential lamination in the complement of K, which remains essential after every non-trivial Dehn surgery along K. Having a persistent lamination implies, for example, that every manifold obtained by non-trivial Dehn surgery along K has universal cover R^3. In this paper we present a method for building persistent laminations for knots from an incompressible Seifert surface for some `parent' knot. Using this construction, we can, for example, currently build persistent laminations for approximately 45 percent of the knots in the standard knot tables; see page 12 of the paper, or http://www.math.unt.edu/~britten/ldt/knots/knotlst1.html, for the exact list.

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