Benson Farb,Dan Margalit's 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 type team Mod(S) is a classical subject that's experiencing a renaissance. It lies on the juncture of geometry, topology, and workforce concept. This publication explains as many vital theorems, examples, and methods as attainable, fast and at once, whereas whilst giving complete info and preserving the textual content approximately self-contained. The booklet is acceptable 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 way in which, vital gadgets and instruments are brought, corresponding to the Birman distinctive series, the advanced of curves, the braid workforce, the symplectic illustration, and the Torelli staff. The publication then introduces Teichmüller area and its geometry, and makes use of the motion of Mod(S) on it to turn out the Nielsen-Thurston type of floor homeomorphisms. subject matters comprise the topology of the moduli house 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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