Vector Braids
| dc.creator | Moulton, Vincent | |
| dc.date | 1994-07-15 | |
| dc.date.accessioned | 2026-07-07T09:14:21Z | |
| dc.date.available | 2026-07-07T09:14:21Z | |
| dc.description | In this paper we define a new family of groups which generalize the {\it classical braid groups on} $\C $. We denote this family by $\{B_n^m\}_{n \ge m+1}$ where $n,m \in \N$. The family $\{ B_n^1 \}_{n \in \N}$ is the set of classical braid groups on $n$ strings. The group $B_n^m$ is the set of motions of $n$ unordered points in $\C^m$, so that at any time during the motion, each $m+1$ of the points span the whole of $\C^m$ as an affine space. There is a map from $B_n^m$ to the symmetric group on $n$ letters. We let $P_n^m$ denote the kernel of this map. In this paper we are mainly interested in understanding $P_n^2$. We give a presentation of a group $PL_n$ which maps surjectively onto $P_n^2$. We also show the surjection $PL_n \to P_n^2$ induces an isomorphism on first and second integral homology and conjecture that it is an isomorphism. We then find an infinitesimal presentation of the group $P_n^2$. Finally, we also consider the analagous groups where points lie in $¶^m$ instead of $\C^m$. These groups generalize of the classical braid groups on the sphere. | |
| dc.description | 39 pages | |
| dc.identifier | https://arxiv.org/abs/hep-th/9407094 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9407094 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152641 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Quantum Algebra | |
| dc.title | Vector Braids | |
| dc.type | text |