Dehn surgery and SU(2) representations

par Steven Sivek

vendredi 7 juin 2019, 10:30 → 11:30 Europe/Paris

112 (ICJ)

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 $\mathbb{S}^3$ ; and the construction of one-cusped hyperbolic 3-manifolds that have many $SU(2)$-cyclic Dehn fillings.  This is joint work with Raphael Zentner.