Volume bounds for generalized twisted torus links

Details Volume bounds for generalized twisted torus links Volume bounds for generalized twisted torus links

2010-07-17

arxiv.org/abs/1007.2932v5

Mathematics

Geometric Topology

Revised version to appear in Mathematical Research Letters. 21 pages, 14 figures

Scientific paper

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.

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