• Corpus ID: 202541663

# Asymptotic translation lengths and normal generations of pseudo-Anosov monodromies for fibered 3-manifolds

@article{Baik2019AsymptoticTL,
title={Asymptotic translation lengths and normal generations of pseudo-Anosov monodromies for fibered 3-manifolds},
author={Hyungryul Baik and E. Kin and Hyunshik Shin and Chenxi Wu},
journal={arXiv: Geometric Topology},
year={2019}
}
• Published 3 September 2019
• Mathematics
• arXiv: Geometric Topology
Let $M$ be a hyperbolic fibered 3-manifold. We study properties of sequences $(S_{\alpha_n}, \psi_{\alpha_n})$ of fibers and monodromies for primitive integral classes in the fibered cone of $M$. The main tool is the asymptotic translation length $\ell_{\mathcal{C}} (\psi_{\alpha_n})$ of the pseudo-Anosov monodromy $\psi_{\alpha_n}$ on the curve complex. We first show that there exists a constant $C>0$ depending only on the fibered cone such that for any primitive integral class $(S, \psi)$ in…
7 Citations

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• 2018
We study the asymptotic behavior of the asymptotic translation lengths on the curve complexes of pseudo-Anosov monodromies in a fibered cone of a fibered hyperbolic 3-manifold $M$ with $b_1(M) \geq • Mathematics Commentarii Mathematici Helvetici • 2022 We provide a simple criterion for an element of the mapping class group of a closed surface to have normal closure equal to the whole mapping class group. We apply this to show that every nontrivial We show that the cone over a fibered face of a compact fibered hyperbolic 3-manifold is dual to the cone generated by the homology classes of finitely many curves called minimal stable loops living • Mathematics Glasnik Matematicki • 2022 We investigate the relation between the topological entropy of pseudo-Anosov maps on surfaces with punctures and the rank of the first homology of their mapping tori. On the surface $$S$$ of genus • Mathematics • 2021 In this article, we study the normal generation of the mapping class group. We first show that a mapping class is normal generator if its restriction on the invariant subsurface normally generates • Mathematics • 2021 . Let S g be a closed orientable surface of genus g > 1. We consider the minimal asymptotic translation length L T ( k, g ) on the Teichm¨uller space of S g , among pseudo-Anosov mapping classes of S • Mathematics • 2020 In this paper, we study the asymptotic translation lengths on the sphere complexes. We first define the generalized fibered cone for a general compact mapping torus, which is a higher-dimensional ## References SHOWING 1-10 OF 36 REFERENCES • Mathematics Groups, Geometry, and Dynamics • 2019 Let$M$be a hyperbolic fibered 3-manifold with$b_1(M) \geq 2$and let$S$be a fiber with pseudo-Anosov monodromy$\psi$. We show that there exists a sequence$(R_n, \psi_n)$of fibers and We study the magic manifold$N$which is a hyperbolic and fibered$3$-manifold. We give an explicit construction of a fiber$F_a$and its monodromy$:F_a \rightarrow F_a$of the fibration associated • Mathematics, Computer Science • 2015 A new construction of ratio optimizers is introduced and they are shown to be found arbitrarily deep into the Johnson filtration as well as in the point pushing subgroup. • Mathematics • 2006 The theme of this paper is that algebraic complexity implies dynamical complexity for pseudo-Anosov homeomorphisms of a closed surface$S_g$of genus$g$. Penner proved that the logarithm of the Given a 3-manifold$M$fibering over the circle, we investigate how the asymptotic translation lengths of pseudo-Anosov monodromies in the arc complex vary as we vary the fibration. We formalize this • Mathematics, Computer Science International Mathematics Research Notices • 2018 In this paper, we show that the minimal asymptotic translation length of the Torelli group${\mathcal{I}}_g$of the surface$S_g$of genus$g$on the curve graph asymptotically behaves like$1/g$, The curve graph,$\mathcal{G}\$, associated to a compact surface Σ is the 1-skeleton of the curve complex defined by Harvey. Masur and Minsky showed that this graph is hyperbolic and defined the
• Mathematics
• 2008
We consider a hyperbolic surface bundle over the circle with the smallest known volume among hyperbolic manifolds having 3 cusps, so called "the magic manifold". We compute the entropy function on