By Benson Farb,Dan Margalit

ISBN-10: 0691147949

ISBN-13: 9780691147949

The examine 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 concept. This publication explains as many vital theorems, examples, and methods as attainable, speedy and at once, whereas even as giving complete information and conserving the textual content approximately self-contained. The e-book is acceptable for graduate students.

A Primer on Mapping category Groups starts off via explaining the most group-theoretical homes of Mod(S), from finite new release by way of Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. alongside the best way, significant items and instruments are brought, reminiscent of the Birman precise series, the complicated of curves, the braid crew, the symplectic illustration, and the Torelli workforce. 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 class of floor homeomorphisms. subject matters comprise the topology of the moduli area of Riemann surfaces, the relationship with floor bundles, pseudo-Anosov conception, 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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