By Benson Farb,Dan Margalit
The research of the mapping category crew Mod(S) is a classical subject that's experiencing a renaissance. It lies on the juncture of geometry, topology, and team thought. This publication explains as many vital theorems, examples, and strategies as attainable, speedy and at once, whereas whilst giving complete information and holding the textual content approximately self-contained. The booklet is appropriate for graduate students.
A Primer on Mapping type Groups starts by means of explaining the most group-theoretical homes of Mod(S), from finite iteration via Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. alongside the way in which, relevant items and instruments are brought, reminiscent of the Birman special series, the complicated of curves, the braid workforce, 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 category of floor homeomorphisms. subject matters 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