By Benson Farb,Dan Margalit
The learn of the mapping category workforce Mod(S) is a classical subject that's experiencing a renaissance. It lies on the juncture of geometry, topology, and crew thought. This publication explains as many vital theorems, examples, and methods as attainable, quick and without delay, whereas whilst giving complete information and preserving the textual content approximately self-contained. The e-book is acceptable for graduate students.
A Primer on Mapping type Groups starts by means of explaining the most group-theoretical houses of Mod(S), from finite iteration by means of Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. alongside the way in which, principal items and instruments are brought, akin to the Birman certain series, the complicated of curves, the braid workforce, the symplectic illustration, and the Torelli crew. The e-book then introduces Teichmüller house and its geometry, and makes use of the motion of Mod(S) on it to end up the Nielsen-Thurston category of floor homeomorphisms. issues comprise the topology of the moduli area of Riemann surfaces, the relationship with floor bundles, pseudo-Anosov idea, and Thurston's method of the classification.
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Extra resources for A Primer on Mapping Class Groups (PMS-49) (Princeton Mathematical Series)
A Primer on Mapping Class Groups (PMS-49) (Princeton Mathematical Series) by Benson Farb,Dan Margalit