Ropelength, crossing number and finite type invariants of links

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 generalizing 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.

arXiv comment16 pages, 6 figures (accepted for publication), corrected: proofs of Theorem B, Lemma F, and constants in the estimates of Theorem A

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• Tree invariants and Milnor linking numbers with indeterminacy
• Diagram complexes, formality, and configuration space integrals for braids