Bipyramid Decompositions of Multi-crossing Link Complements

2016/10/12 by Adams, Colin, Kehne, Gregory
#57M50 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1610.03830

Abstract

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

Related

• Bipyramids and bounds on volumes of hyperbolic links
• Generalized bipyramids and hyperbolic volumes of tiling links
• Triple Crossing Number of Knots and Links
• Generalized bipyramids and hyperbolic volumes of alternating k-uniform tiling links
• Volume conjecture, geometric decomposition and deformation of hyperbolic structures