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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