Get A Primer on Mapping Class Groups (PMS-49) (Princeton PDF

By Benson Farb,Dan Margalit

The examine 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 idea. This ebook explains as many very important theorems, examples, and methods as attainable, fast and at once, whereas even as giving complete information and holding the textual content approximately self-contained. The booklet is acceptable for graduate students.

A Primer on Mapping classification Groups starts off by way of explaining the most group-theoretical houses of Mod(S), from finite new release via Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. alongside the way in which, valuable gadgets and instruments are brought, reminiscent of the Birman unique series, the complicated of curves, the braid workforce, the symplectic illustration, and the Torelli workforce. The publication then introduces Teichmüller area and its geometry, and makes use of the motion of Mod(S) on it to end up the Nielsen-Thurston type 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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