Winding numbers and SU(2)-representations of knot groups
| dc.creator | Bowden, Dylan | |
| dc.creator | Howie, James | |
| dc.date | 2007-06-07 | |
| dc.date.accessioned | 2026-07-07T08:04:27Z | |
| dc.date.available | 2026-07-07T08:04:27Z | |
| dc.description | Given an abelian group $A$ and a Lie group $G$, we construct a bilinear pairing from $A\timesπ_1({\mathcal R})$ to $π_1(G)$, where $\mathcal R$ is a subvariety of the variety of representations $A\to G$. In the case where $A$ is the peripheral subgroup of a torus or two-bridge knot group, $G=S^1$ and $\mathcal R$ is a certain variety of representations arising from suitable SU(2)-representations of the knot group, we show that this pairing is not identically zero. We discuss the consequences of this result for the SU(2)-representations of fundamental groups of manifolds obtained by Dehn surgery on such knots. | |
| dc.description | 13 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/0706.0957 | |
| dc.identifier | http://arxiv.org/abs/0706.0957 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129968 | |
| dc.subject | Geometric Topology | |
| dc.subject | Group Theory | |
| dc.subject | 57M25; 20F05, 20G05 | |
| dc.title | Winding numbers and SU(2)-representations of knot groups | |
| dc.type | text |