SU(2)-Cyclic Surgeries on Knots. (24th November 2015) - Lin, Jianfeng
Abstract : A surgery on a knot in S^3 is called SU(2) -cyclic if it gives a manifold whose fundamental group has no noncyclic SU(2) representations. Using holonomy perturbations on the Chern–Simons functional, we prove that two SU(2) -cyclic surgery coefficients p_1q_1 and p_2q_2 should satisfy |p_1q_2-p_2q_1|≤ |p_1|+|p_2| . This is an analog of Culler–Gordon–Luecke–Shalen's cyclic surgery theorem.