Braids and partial permutations

James East

doi:10.1016/j.aim.2007.01.002

Braids and partial permutations

James East

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

We study the inverse braid monoid IBn introduced by Easdown and Lavers in 2004. We completely describe the factorizable structure of IBn and use this to give a new proof of the Easdown–Lavers presentation; we also derive several new presentations, each of which gives rise to a new presentation of the symmetric inverse monoid. We then define and study the pure inverse braid monoid IPn which is related to IBn in the same way that the pure braid group is related to the braid group.

Original language	English
Pages (from-to)	440-461
Number of pages	22
Journal	Advances in Mathematics
Volume	213
Issue number	1
DOIs	https://doi.org/10.1016/j.aim.2007.01.002
Publication status	Published - 2007

Keywords

braid theory
monoids

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10.1016/j.aim.2007.01.002

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abstract = "We study the inverse braid monoid IBn introduced by Easdown and Lavers in 2004. We completely describe the factorizable structure of IBn and use this to give a new proof of the Easdown–Lavers presentation; we also derive several new presentations, each of which gives rise to a new presentation of the symmetric inverse monoid. We then define and study the pure inverse braid monoid IPn which is related to IBn in the same way that the pure braid group is related to the braid group.",

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AB - We study the inverse braid monoid IBn introduced by Easdown and Lavers in 2004. We completely describe the factorizable structure of IBn and use this to give a new proof of the Easdown–Lavers presentation; we also derive several new presentations, each of which gives rise to a new presentation of the symmetric inverse monoid. We then define and study the pure inverse braid monoid IPn which is related to IBn in the same way that the pure braid group is related to the braid group.

KW - braid theory

KW - monoids

UR - http://handle.uws.edu.au:8081/1959.7/uws:28964

U2 - 10.1016/j.aim.2007.01.002

DO - 10.1016/j.aim.2007.01.002

M3 - Article

SN - 0001-8708

VL - 213

SP - 440

EP - 461

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 1

ER -

Braids and partial permutations

Abstract

Keywords

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