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Simplicial volume of links from link diagrams

Published online by Cambridge University Press:  06 November 2017

OLIVER DASBACH
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803, U.S.A. e-mail: kasten@math.lsu.edu
ANASTASIIA TSVIETKOVA
Affiliation:
Department of Mathematics and Computer Science, 360 Dr. Martin Luther King Jr. Blvd., Hill Hall 325, Newark, NJ 07102, U.S.A e-mail: n.tsvet@gmail.com

Abstract

The hyperbolic volume of a link complement is known to be unchanged when a half-twist is added to a link diagram, and a suitable 3-punctured sphere is present in the complement. We generalise this to the simplicial volume of link complements by analysing the corresponding toroidal decompositions. We then use it to prove a refined upper bound for the volume in terms of twists of various lengths for links.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2017 

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References

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