Conjugacy for positive permutation braids

• Autorzy: Hugh R. Morton , Richard J. Hadji
• Języki publikacji: EN

Abstrakty

EN

Positive permutation braids on n strings, which are defined to be positive n-braids where each pair of strings crosses at most once, form the elementary but non-trivial building blocks in many studies of conjugacy in the braid groups. We consider conjugacy among these elementary braids which close to knots, and show that those which close to the trivial knot or to the trefoil are all conjugate. All such n-braids with the maximum possible crossing number are also shown to be conjugate.
We note that conjugacy of these braids for n ≤ 5 depends only on the crossing number. In contrast, we exhibit two such braids on 6 strings with 9 crossings which are not conjugate but whose closures are each isotopic to the (2,5) torus knot.

Kategorie tematyczne

• 57M25: Knots and links in S 3

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2005
• Tom: 188
• Numer: 1
• Strony: 155-166

Daty

wydano

2005

Twórcy

autor

Hugh R. Morton

• Department of Mathematical Sciences, University of Liverpool, Peach St., Liverpool, L69 7ZL, England

autor

Richard J. Hadji

• Department of Mathematical Sciences, University of Liverpool, Peach St Liverpool, L69 7ZL, England

Identyfikatory

DOI

10.4064/fm188-0-8