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By Benson Farb,Dan Margalit

The research of the mapping classification crew Mod(S) is a classical subject that's experiencing a renaissance. It lies on the juncture of geometry, topology, and staff thought. This ebook explains as many vital theorems, examples, and strategies as attainable, quick and at once, whereas while giving complete information and conserving the textual content approximately self-contained. The booklet is appropriate for graduate students.

A Primer on Mapping category Groups starts through explaining the most group-theoretical homes of Mod(S), from finite iteration through Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. alongside the best way, relevant items and instruments are brought, resembling the Birman certain series, the advanced of curves, the braid crew, the symplectic illustration, and the Torelli team. The booklet then introduces Teichmüller area and its geometry, and makes use of the motion of Mod(S) on it to turn out the Nielsen-Thurston category of floor homeomorphisms. subject matters comprise 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


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