Arc-presentations of links: Monotonic simplification

• Autorzy: I. A. Dynnikov
• Języki publikacji: EN

Abstrakty

EN

In the early 90's J. Birman and W. Menasco worked out a nice technique for studying links presented in the form of a closed braid. The technique is based on certain foliated surfaces and uses tricks similar to those that were introduced earlier by D. Bennequin. A few years later P. Cromwell adapted Birman-Menasco's method for studying so-called arc-presentations of links and established some of their basic properties. Here we further develop that technique and the theory of arc-presentations, and prove that any arc-presentation of the unknot admits a (non-strictly) monotonic simplification by elementary moves; this yields a simple algorithm for recognizing the unknot. We also show that the problem of recognizing split links and that of factorizing a composite link can be solved in a similar manner. We also define two easily checked sufficient conditions for knottedness.

Kategorie tematyczne

• 57M25: Knots and links in S 3

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2006
• Tom: 190
• Numer: 1
• Strony: 29-76

Daty

wydano

2006

Twórcy

autor

I. A. Dynnikov

• Department of Mechanics and Mathematics, Moscow State University, Moscow 119992 GSP-2, Russia

Identyfikatory

DOI

10.4064/fm190-0-3