A presentation for Hilden's subgroup of the braid group

Stephen Tawn

doi:10.4310/MRL.2008.v15.n6.a16

A presentation for Hilden's subgroup of the braid group

Stephen Tawn

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

9 Citations (Scopus)

Abstract

Consider the unit ball, B = Dx[0, 1], containing n unknotted arcs a1, . . . , an such that the boundary of each ai lies in D x {0}. We give a finite presentation for the mapping class group of B fixing the arcs {a1, . . . , an} setwise and fixing D x {1} pointwise. This presentation is calculated using the action of this group on a simply-connected complex.

Original language	English
Pages (from-to)	1277-1293
Number of pages	17
Journal	Mathematical Research Letters
Volume	15
Issue number	6
DOIs	https://doi.org/10.4310/MRL.2008.v15.n6.a16
Publication status	Published - 2008

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10.4310/MRL.2008.v15.n6.a16

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abstract = "Consider the unit ball, B = Dx[0, 1], containing n unknotted arcs a1, . . . , an such that the boundary of each ai lies in D x {0}. We give a finite presentation for the mapping class group of B fixing the arcs {a1, . . . , an} setwise and fixing D x {1} pointwise. This presentation is calculated using the action of this group on a simply-connected complex.",

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AU - Tawn, Stephen

PY - 2008

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N2 - Consider the unit ball, B = Dx[0, 1], containing n unknotted arcs a1, . . . , an such that the boundary of each ai lies in D x {0}. We give a finite presentation for the mapping class group of B fixing the arcs {a1, . . . , an} setwise and fixing D x {1} pointwise. This presentation is calculated using the action of this group on a simply-connected complex.

AB - Consider the unit ball, B = Dx[0, 1], containing n unknotted arcs a1, . . . , an such that the boundary of each ai lies in D x {0}. We give a finite presentation for the mapping class group of B fixing the arcs {a1, . . . , an} setwise and fixing D x {1} pointwise. This presentation is calculated using the action of this group on a simply-connected complex.

UR - http://handle.uws.edu.au:8081/1959.7/546699

U2 - 10.4310/MRL.2008.v15.n6.a16

DO - 10.4310/MRL.2008.v15.n6.a16

M3 - Article

SN - 1073-2780

VL - 15

SP - 1277

EP - 1293

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 6

ER -

A presentation for Hilden's subgroup of the braid group

Abstract

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