Mutual braiding and the band presentation of braid groups

Morton, HR ORCID: 0000-0002-8524-2695 and Rampichini, M
(1999) Mutual braiding and the band presentation of braid groups. In: Knots in Hellas '98: Proceedings of the International Conference on Knot Theory and its Ramifications. World Scientific,Singapore, pp. 335-346. ISBN 978-981-4492-87-4

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This paper is concerned with detecting when a closed braid and its axis are 'mutually braided' in the sense of Rudolph. It deals with closed braids which are fibred links, the simplest case being closed braids which present the unknot. The geometric condition for mutual braiding refers to the existence of a close control on the way in which the whole family of fibre surfaces meet the family of discs spanning the braid axis. We show how such a braid can be presented naturally as a word in the `band generators' of the braid group discussed by Birman, Ko and Lee in their recent account of the band presentation of the braid groups. In this context we are able to convert the conditions for mutual braiding into the existence of a suitable sequence of band relations and other moves on the braid word, and derive a combinatorial method for deciding whether a braid is mutually braided.

Item Type: Book Section
Additional Information: 13 pages, 10 figures. To appear in the proceedings of 'Knots in Hellas 98'
Uncontrolled Keywords: math.GT, math.GT, 57M25
Depositing User: Symplectic Admin
Date Deposited: 26 Jan 2016 12:50
Last Modified: 17 Dec 2022 01:38
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