Volumes of highly twisted knots and links
几何拓扑
2014-10-01 v2
摘要
We show that for a large class of hyperbolic knots and links, we can determine bounds on the volume of the link complement from combinatorial information given by a link diagram. Specifically, there is a universal constant C such that if a knot or link admits a prime, twist reduced diagram with at least 2 twist regions and at least C crossings per twist region, then the link complement is hyperbolic with volume bounded below by 3.3515 times the number of twist regions in the diagram. C is at most 113.
引用
@article{arxiv.math/0604476,
title = {Volumes of highly twisted knots and links},
author = {Jessica S. Purcell},
journal= {arXiv preprint arXiv:math/0604476},
year = {2014}
}
备注
14 pages, 4 figures. Minor changes to clarify exposition, fix typos, and correct a historical inaccuracy in the introduction. Paper has now appeared in AGT