Geometry and Topology Seminar
A 3-manifold is said to be SU(2)-cyclic if every representation of its fundamental group into SU(2) has cyclic image. We will use this notion to discuss several questions about Dehn surgery. These include a proof, free of any gauge theory or Floer homology, that infinitely many 3-manifolds with weight-one fundamental group cannot be constructed by Dehn surgery on a knot in S^3; and the construction of one-cusped hyperbolic 3-manifolds that have many SU(2)-cyclic Dehn fillings. This is joint work with Raphael Zentner.