Geodesic
Ropelength, crossing number and finite-type invariants of links
Komendarczyk, Rafal1 ; Michaelides, Andreas2
1 Department of Mathematics, Tulane University, New Orleans, LA, United States
2 Department of Mathematics, University of South Alabama, Mobile, AL, United States
Algebraic and Geometric Topology, Tome 19 (2019) no. 7, pp. 3335-3357

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2019.19.3335
Classification : 57M25, 53A04
Keywords: knots, links, ropelength, thickness, finite type invariants

Komendarczyk, Rafal 1 ; Michaelides, Andreas 2

1 Department of Mathematics, Tulane University, New Orleans, LA, United States
2 Department of Mathematics, University of South Alabama, Mobile, AL, United States 
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Komendarczyk, Rafal; Michaelides, Andreas. Ropelength, crossing number and finite-type invariants of links. Algebraic and Geometric Topology, Tome 19 (2019) no. 7, pp. 3335-3357. doi: 10.2140/agt.2019.19.3335

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