Closed essential surfaces in the complements of large volume Berge knots

Details Closed essential surfaces in the complements of large volume Berge knots Closed essential surfaces in the complements of large volume Berge knots

2005-09-04

arxiv.org/abs/math/0509082v1

Mathematics

Geometric Topology

41 pages, 11 figures

Scientific paper

We construct an algorithm that lists all closed essential surfaces in the complement of a knot that lies on the fiber of a trefoil or figure eight knot. Such knots are Berge knots and hence admit lens space surgeries. Furthermore they may have arbitrarily large hyperbolic volume. Using this algorithm we concoct large volume Berge knots of two flavors: those whose complement contains arbitrarily many distinct closed essential surfaces, and those whose complement contains no closed essential surfaces.

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