Conjugacy for positive permutation braids

Morton, HR ORCID: 0000-0002-8524-2695 and Hadji, RJ (2005) Conjugacy for positive permutation braids. FUNDAMENTA MATHEMATICAE, 188. pp. 155-166.

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Abstract

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<6 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.

Item Type:	Article
Additional Information:	## TULIP Type: Articles/Papers (Journal) ##
Uncontrolled Keywords:	positive permutation braids, conjugacy, cycles
Depositing User:	Symplectic Admin
Date Deposited:	22 Apr 2016 14:14
Last Modified:	15 Dec 2022 07:32
DOI:	10.4064/fm188-0-8
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3000531