A PRESENTATION FOR THE PURE HILDEN GROUP

作者：Tawn Stephen^*

来源：Mathematical Research Letters, 2013, 20(1): 195-216.

DOI：10.4310/mrl.2013.v20.n1.a14

Consider the half ball, B-+(3), containing n unknotted and unlinked arcs a(1), a(2),..., an such that the boundary of each a(i) lies in the plane. The Hilden (or Wicket) group is the mapping class group of B-+(3) fixing the arcs a(1) boolean OR a(2) boolean OR ... boolean OR a(n) setwise and fixing the half sphere S-+(2) pointwise. This group can be considered as a subgroup of the braid group on 2n strands. 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 presentation 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.

• 出版日期2013