#### Volume 19, issue 7 (2019)

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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
Primary: 57M25
Secondary: 53A04