# 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} }

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…

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