Volume bounds for generalized twisted torus links
Geometric Topology
2014-05-20 v5
Abstract
Twisted torus knots and links are given by twisting adjacent strands of a torus link. They are geometrically simple and contain many examples of the smallest volume hyperbolic knots. Many are also Lorenz links. We study the geometry of twisted torus links and related generalizations. We determine upper bounds on their hyperbolic volumes that depend only on the number of strands being twisted. We exhibit a family of twisted torus knots for which this upper bound is sharp, and another family with volumes approaching infinity. Consequently, we show there exist twisted torus knots with arbitrarily large braid index and yet bounded volume.
Cite
@article{arxiv.1007.2932,
title = {Volume bounds for generalized twisted torus links},
author = {Abhijit Champanerkar and David Futer and Ilya Kofman and Walter Neumann and Jessica S. Purcell},
journal= {arXiv preprint arXiv:1007.2932},
year = {2014}
}
Comments
Revised version to appear in Mathematical Research Letters. 21 pages, 14 figures