A presentation for Hilden's subgroup of the braid group
Abstract
Consider the unit ball, B = D x [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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