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

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

2007-06-07

arxiv.org/abs/0706.0957v1

Mathematics

Geometric Topology

13 pages, 2 figures

Scientific paper

Given an abelian group $A$ and a Lie group $G$, we construct a bilinear pairing from $A\times\pi_1({\mathcal R})$ to $\pi_1(G)$, 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.

Affiliated with

Also associated with

No associations

Rating

Winding numbers and SU(2)-representations of knot groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Winding numbers and SU(2)-representations of knot groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Winding numbers and SU(2)-representations of knot groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-441986