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A Primer on Mapping Class Groups (PMS-49) by Dan Margalit, Benson Farb

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Chapter Fourteen

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Pseudo-Anosov Theory

The power of the Nielsen–Thurston classification is that it gives a simple criterion for an element f euro Mod(S) to be pseudo-Anosov: f is neither finite-order nor reducible. This fact, however, is only as useful as the depth of our knowledge of pseudo-Anosov homeomorphisms. The purpose of this chapter is to study pseudo-Anosov homeomorphisms: their construction, their algebraic properties, and their dynamical properties.

Anosov maps of the torus. An Anosov homeomorphism of the torus T2 is a linear representative ...

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