SU(2)-Cyclic Surgeries on Knots. (24th November 2015) - Lin, Jianfeng
Abstract : A surgery on a knot in $S^{3}$ is called ${\rm SU}(2)$ -cyclic if it gives a manifold whose fundamental group has no noncyclic ${\rm SU}(2)$ representations. Using holonomy perturbations on the Chern–Simons functional, we prove that two ${\rm SU}(2)$ -cyclic surgery coefficients $\frac {p_{1}}{q_{1}}$ and $\frac {p_{2}}{q_{2}}$ should satisfy $|p_{1}q_{2}-p_{2}q_{1}|\leq |p_{1}|+|p_{2}|$ . This is an analog of Culler–Gordon–Luecke–Shalen's cyclic surgery theorem.