Graphs, determinants of knots and hyperbolic volume

Alexander Stoimenow

Vol. 232 (2007), No. 2, 423–451

DOI: 10.2140/pjm.2007.232.423

Abstract

Using estimates for the number of spanning trees of planar graphs, we prove inequalities for the determinant of alternating links in terms of their hyperbolic volume.

Keywords

alternating knot, determinant, spanning tree, planar graph, hyperbolic volume

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 05C05, 05C62, 57M12, 57M50

Milestones

Received: 24 May 2006

Revised: 29 July 2007

Accepted: 30 July 2007

Published: 1 October 2007