Winding numbers and SU(2)-representations of knot groups

dc.creatorBowden, Dylan
dc.creatorHowie, James
dc.date2007-06-07
dc.date.accessioned2026-07-07T08:04:27Z
dc.date.available2026-07-07T08:04:27Z
dc.descriptionGiven 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.description13 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/0706.0957
dc.identifierhttp://arxiv.org/abs/0706.0957
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/129968
dc.subjectGeometric Topology
dc.subjectGroup Theory
dc.subject57M25; 20F05, 20G05
dc.titleWinding numbers and SU(2)-representations of knot groups
dc.typetext

Files

Collections