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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Examples of pseudo-Anosov homeomorphisms


Author: Max Bauer
Journal: Trans. Amer. Math. Soc. 330 (1992), 333-359
MSC: Primary 57M99; Secondary 57N05, 57R50, 58F15
MathSciNet review: 1094557
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Abstract: We generalize a construction in knot theory to construct a large family $ \mathcal{G}\mathcal{R} = \cup \,GR(\mathcal{P})$ of mapping classes of a surface of genus $ g$ and one boundary component, where $ \mathcal{P}$ runs over some finite index set. We exhibit explicitly the set $ \mathcal{G}{\mathcal{R}^{\ast}} \subset \mathcal{G}\mathcal{R}$ that consists of pseudo-Anosov maps, find the map that realizes the smallest dilatation in $ \mathcal{G}{\mathcal{R}^{\ast}}$, and for every $ \mathcal{P}$, we give a set of defining relations for $ GR(\mathcal{P})$.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1094557-8
Article copyright: © Copyright 1992 American Mathematical Society