By Benson Farb
The learn of the mapping category staff Mod(S) is a classical subject that's experiencing a renaissance. It lies on the juncture of geometry, topology, and team conception. This e-book explains as many vital theorems, examples, and strategies as attainable, fast and at once, whereas even as giving complete info and preserving the textual content approximately self-contained. The publication is appropriate for graduate students.
A Primer on Mapping classification Groups starts off through explaining the most group-theoretical houses of Mod(S), from finite iteration via Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. alongside the way in which, imperative items and instruments are brought, equivalent to the Birman specific series, the advanced of curves, the braid team, the symplectic illustration, and the Torelli team. The ebook then introduces Teichmüller house and its geometry, and makes use of the motion of Mod(S) on it to turn out the Nielsen-Thurston class of floor homeomorphisms. themes contain the topology of the moduli area of Riemann surfaces, the relationship with floor bundles, pseudo-Anosov idea, and Thurston's method of the classification.
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