Communications in Analysis and Geometry

Volume 28 (2020)

Number 3

Bipyramid decompositions of multicrossing link complements

Pages: 499 – 518

DOI: https://dx.doi.org/10.4310/CAG.2020.v28.n3.a1

Authors

Colin Adams (Department of Mathematics and Statistics, Williams College, Williamstown, Massachusetts, U.S.A.)

Gregory Kehne (Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania, U.S.A.)

Abstract

Generalizing previous constructions, we present a dual pair of decompositions of the complement of a link $L$ into bipyramids, given any multicrossing projection of $L$. When $L$ is hyperbolic, this gives new upper bounds on the volume of $L$ given its multicrossing projection. These bounds are realized by three closely related infinite tiling weaves.

Full Text (PDF format)

Received 17 November 2016

Accepted 22 December 2017

Published 6 July 2020