Number Theory

New PDF release: A Primer on Mapping Class Groups (PMS-49) (Princeton

By Benson Farb,Dan Margalit

ISBN-10: 0691147949

ISBN-13: 9780691147949

The examine of the mapping classification workforce Mod(S) is a classical subject that's experiencing a renaissance. It lies on the juncture of geometry, topology, and crew conception. This publication explains as many vital theorems, examples, and methods as attainable, fast and at once, whereas even as giving complete info and preserving the textual content approximately self-contained. The e-book 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 iteration through Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. alongside the way in which, critical items and instruments are brought, equivalent to the Birman specified series, the advanced of curves, the braid workforce, the symplectic illustration, and the Torelli crew. 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 class of floor homeomorphisms. themes 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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