A Menagerie of SU(2)-Cyclic 3-Manifolds
| Autor: | Raphael Zentner, Steven Sivek |
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| Rok vydání: | 2021 |
| Předmět: |
Fundamental group
Pure mathematics General Mathematics Image (category theory) Fibered manifold 010102 general mathematics Representation (systemics) Lens space Geometric Topology (math.GT) Menagerie Mathematics::Geometric Topology 01 natural sciences 0101 Pure Mathematics Mathematics - Geometric Topology 0103 physical sciences FOS: Mathematics math.GT 010307 mathematical physics 0101 mathematics Abelian group Mathematics::Symplectic Geometry Special unitary group Mathematics |
| Zdroj: | International Mathematics Research Notices. 2022:8038-8085 |
| ISSN: | 1687-0247 1073-7928 |
| DOI: | 10.1093/imrn/rnaa330 |
| Popis: | 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 which are not hyperbolic. As an application, we give examples of hyperbolic 3-manifolds which 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. Comment: 36 pages, 4 figures. v2: accepted version; added Lemma 2.4 to streamline parts of section 2 |
| Databáze: | OpenAIRE |
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