Communications in Analysis and Geometry

Volume 28 (2020)

Number 3

Bipyramid decompositions of multicrossing link complements

Pages: 499 – 518



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.)


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.

Received 17 November 2016

Accepted 22 December 2017

Published 6 July 2020