Read e-book online A Primer on Mapping Class Groups (PMS-49) (Princeton PDF

By Benson Farb,Dan Margalit

ISBN-10: 0691147949

ISBN-13: 9780691147949

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 crew concept. This booklet explains as many vital theorems, examples, and methods as attainable, quick and at once, whereas even as giving complete information and protecting the textual content approximately self-contained. The booklet is appropriate for graduate students.

A Primer on Mapping classification Groups starts via explaining the most group-theoretical houses of Mod(S), from finite iteration by way of Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. alongside the way in which, critical items and instruments are brought, reminiscent of the Birman special 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 end up the Nielsen-Thurston type of floor homeomorphisms. subject matters comprise the topology of the moduli area of Riemann surfaces, the relationship with floor bundles, pseudo-Anosov concept, 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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