A presentation for the pure Hilden group
| dc.creator | Tawn, Stephen | |
| dc.date | 2009-02-27 | |
| dc.date.accessioned | 2026-07-07T12:47:36Z | |
| dc.date.available | 2026-07-07T12:47:36Z | |
| dc.description | Consider the unit ball, $B = D \times [0,1]$, containing $n$ unknotted arcs $a_1, a_2, ..., a_n$ such that the boundary of each $a_i$ lies in $D \times \{0\}$. The Hilden (or Wicket) group is the mapping class group of $B$ fixing the arcs $a_1 \cup a_2 \cup ... \cup a_n$ setwise and fixing $D \times \{1\}$ 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. | |
| dc.description | 26 pages | |
| dc.identifier | https://arxiv.org/abs/0902.4840 | |
| dc.identifier | http://arxiv.org/abs/0902.4840 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221774 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | 20F05; 57M07; 20F36; 57M60 | |
| dc.title | A presentation for the pure Hilden group | |
| dc.type | text |