Affiliation:
1. Department of Mathematics, Imperial College London 180 Queen's Gate London SW7 2AZ United Kingdom
2. Fakultät für Mathematik, Universität Regensburg 93040 Regensburg Germany
Abstract
Abstract
We classify $SU(2)$-cyclic and $SU(2)$-abelian 3-manifolds, for which every representation of the fundamental group into $SU(2)$ has cyclic or abelian image, respectively, among geometric 3-manifolds that are not hyperbolic. As an application, we give examples of hyperbolic 3-manifolds that do not admit degree-1 maps to any Seifert Fibered manifold other than $S^3$ or a lens space. We also produce infinitely many one-cusped hyperbolic manifolds with at least four $SU(2)$-cyclic Dehn fillings, one more than the number of cyclic fillings allowed by the cyclic surgery theorem.
Publisher
Oxford University Press (OUP)
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