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2006 | 190 | 1 | 29-76
Tytuł artykułu

Arc-presentations of links: Monotonic simplification

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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.
Słowa kluczowe
Kategorie tematyczne
Rocznik
Tom
190
Numer
1
Strony
29-76
Opis fizyczny
Daty
wydano
2006
Twórcy
  • Department of Mechanics and Mathematics, Moscow State University, Moscow 119992 GSP-2, Russia
Bibliografia
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-fm190-0-3
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