By Benson Farb,Dan Margalit
The research of the mapping category crew Mod(S) is a classical subject that's experiencing a renaissance. It lies on the juncture of geometry, topology, and team concept. This booklet explains as many vital theorems, examples, and methods as attainable, fast and without delay, 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 category Groups starts by way of explaining the most group-theoretical homes of Mod(S), from finite new release by means of Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. alongside the best way, relevant items and instruments are brought, similar to the Birman designated series, the advanced of curves, the braid staff, the symplectic illustration, and the Torelli workforce. The publication then introduces Teichmüller house and its geometry, and makes use of the motion of Mod(S) on it to turn out the Nielsen-Thurston category of floor homeomorphisms. issues 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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A Primer on Mapping Class Groups (PMS-49) (Princeton Mathematical Series) by Benson Farb,Dan Margalit