Combinatorics of link diagrams and volume

@article{Giambrone2013CombinatoricsOL,
  title={Combinatorics of link diagrams and volume},
  author={Adam Giambrone},
  journal={Journal of Knot Theory and Its Ramifications},
  year={2013},
  volume={24},
  pages={1550001}
}
  • A. Giambrone
  • Published 31 October 2013
  • Mathematics
  • Journal of Knot Theory and Its Ramifications
We show that the volumes of certain hyperbolic A-adequate links can be bounded (above and) below in terms of two diagrammatic quantities: the twist number and the number of certain alternating tangles in an A-adequate diagram. We then restrict our attention to plat closures of certain braids, a rich family of links whose volumes can be bounded in terms of the twist number alone. Furthermore, in the absence of special tangles, our volume bounds can be expressed in terms of a single stable… 
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