English

Closed essential surfaces in the complements of large volume Berge knots

Geometric Topology 2007-05-23 v1

Abstract

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.

Keywords

Cite

@article{arxiv.math/0509082,
  title  = {Closed essential surfaces in the complements of large volume Berge knots},
  author = {Kenneth L. Baker},
  journal= {arXiv preprint arXiv:math/0509082},
  year   = {2007}
}

Comments

41 pages, 11 figures