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Ropelength, crossing
number and finite-type invariants of links
Rafal Komendarczyk and Andreas Michaelides |
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Algebraic & Geometric Topology 19 (2019) 3335–3357
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Abstract |
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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 –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. |
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Keywords
knots, links, ropelength, thickness, finite type invariants
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Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 53A04
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References |
Publication
Received: 30 December 2017
Revised: 31 July 2018
Accepted: 31 October 2018
Published: 17 December 2019
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Authors |
| Rafal Komendarczyk | |
| Department of Mathematics Tulane University New Orleans, LA United States |
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| Andreas Michaelides | |
| Department of Mathematics University of South Alabama Mobile, AL United States |
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