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Ropelength, crossing number and finite-type invariants of links

Rafal Komendarczyk and Andreas Michaelides

Algebraic & Geometric Topology 19 (2019) 3335–3357
Abstract

Ropelength and embedding thickness are related measures of geometric complexity of classical knots and links in Euclidean space. In their recent work, Freedman and Krushkal posed a question regarding lower bounds for embedding thickness of n–component links in terms of the Milnor linking numbers. The main goal of the current paper is to provide such estimates, and thus generalize the known linking number bound. In the process, we collect several facts about finite-type invariants and ropelength/crossing number of knots. We give examples of families of knots where such estimates behave better than the well-known knot–genus estimate.

Keywords
knots, links, ropelength, thickness, finite type invariants
Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 53A04
References
Publication
Received: 30 December 2017
Revised: 31 July 2018
Accepted: 31 October 2018
Published: 17 December 2019
Authors
Rafal Komendarczyk
Department of Mathematics
Tulane University
New Orleans, LA
United States
Andreas Michaelides
Department of Mathematics
University of South Alabama
Mobile, AL
United States