Download A Primer on Mapping Class Groups (PMS-49) (Princeton by Benson Farb,Dan Margalit PDF

By Benson Farb,Dan Margalit

The learn of the mapping type workforce Mod(S) is a classical subject that's experiencing a renaissance. It lies on the juncture of geometry, topology, and staff thought. This booklet explains as many vital theorems, examples, and methods as attainable, speedy and without delay, whereas whilst giving complete info and holding the textual content approximately self-contained. The e-book is appropriate for graduate students.

A Primer on Mapping category Groups starts by means of 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, significant items and instruments are brought, akin to the Birman detailed series, the complicated of curves, the braid team, the symplectic illustration, and the Torelli workforce. The e-book 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. subject matters contain the topology of the moduli area of Riemann surfaces, the relationship with floor bundles, pseudo-Anosov thought, and Thurston's method of the classification.

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