Ropelength, crossing number and finite-type invariants of links

Komendarczyk, Rafal; Michaelides, Andreas

doi:10.2140/agt.2019.19.3335

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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

DOI: 10.2140/agt.2019.19.3335

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

Volume 19, issue 7 (2019)