A presentation for Hilden’s subgroup of the braid group

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A presentation for Hilden’s subgroup of the braid group

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

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ژورنال

عنوان ژورنال: Mathematical Research Letters

سال: 2008

ISSN: 1073-2780,1945-001X

DOI: 10.4310/mrl.2008.v15.n6.a16