A presentation for the pure Hilden group
نویسنده
چکیده
Consider the unit ball, B = D × [0, 1], containing n unknotted arcs a1, a2, . . . , an such that the boundary of each ai lies in D × {0}. The Hilden (or Wicket) group is the mapping class group of B fixing the arcs a1 ∪ a2 ∪ . . . ∪ an setwise and fixing D × {1} pointwise. This group can be considered as a subgroup of the braid group. The pure Hilden group is defined to be the intersection of the Hilden group and the pure braid group. In a previous paper we computed a presentaion for the Hilden group using an action of the group on a cellular complex. This paper uses the same action and complex to calculate a finite presentation for the pure Hilden group. The framed braid group acts on the pure Hilden group by conjugation and this action is used to reduce the number of cases.
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