Topology of knots. (English) Zbl 0799.57003

Scharlemann, Martin

Moffatt, H. K. (ed.) et al., Topological aspects of the dynamics of fluids and plasmas. Proceedings of the program of the Institute for Theoretical Physics, University of California at Santa Barbara, USA and of the NATO advanced research workshop on topological aspects of the dynamics of fluids and plasmas, University of California at Santa Barbara, USA, November 1-5, 1991. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. E, Appl. Sci. 218, 65-82 (1992).

Summary: This is meant to be a gentle introduction to the theory of knots, aimed specifically at physicists who want some background to M. H. Freedman and Z. He’s work [Ann. Math., II. Ser. 134, No. 1, 189- 229 (1991; Zbl 0746.57011)] relating asymptotic crossing number of knots to estimates of the energy in a knotted divergence-free flow.
For the entire collection see [Zbl 0777.00043].

MSC:

57M25

Knots and links in the \(3\)-sphere (MSC2010)

Keywords:

knot energy; bridge number; Seifert surface; winding; band sums; satellites; knots; asymptotic crossing number of knots; energy in a knotted divergence-free flow

Citations:

Zbl 0746.57011