Limits of sequences of pseudo-Anosov maps and of hyperbolic 3–manifolds
| Autor: | Toby Hall, André de Carvalho, Juan González-Meneses, Sylvain Bonnot |
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| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Mathematics::Dynamical Systems TEORIA DOS GRUPOS Closure (topology) Geometric Topology (math.GT) Of the form Type (model theory) Mathematics::Geometric Topology Homeomorphism Mathematics - Geometric Topology Hyperbolic set 57M50 37E30 57M25 20F36 FOS: Mathematics Braid Geometry and Topology Mathematics |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP Algebraic & Geometric Topology |
| ISSN: | 1472-2739 1472-2747 |
| DOI: | 10.2140/agt.2021.21.1351 |
| Popis: | There are two objects naturally associated with a braid $\beta\in B_n$ of pseudo-Anosov type: a (relative) pseudo-Anosov homeomorphism $\varphi_\beta\colon S^2\to S^2$; and the finite volume complete hyperbolic structure on the 3-manifold $M_\beta$ obtained by excising the braid closure of $\beta$, together with its braid axis, from $S^3$. We show the disconnect between these objects, by exhibiting a family of braids $\{\beta_q:q\in{\mathbb{Q}}\cap(0,1/3]\}$ with the properties that: on the one hand, there is a fixed homeomorphism $\varphi_0\colon S^2\to S^2$ to which the (suitably normalized) homeomorphisms $\varphi_{\beta_{q}}$ converge as $q\to 0$; while on the other hand, there are infinitely many distinct hyperbolic 3-manifolds which arise as geometric limits of the form $\lim_{k\to\infty} M_{\beta_{q_k}}$, for sequences $q_k\to 0$. Comment: Author accepted manuscript |
| Databáze: | OpenAIRE |
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