By Benson Farb,Dan Margalit
The research 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 crew thought. This ebook explains as many vital theorems, examples, and strategies as attainable, speedy and without delay, whereas while giving complete info and protecting the textual content approximately self-contained. The publication is appropriate for graduate students.
A Primer on Mapping category Groups starts off through explaining the most group-theoretical homes 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, valuable gadgets and instruments are brought, resembling 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 turn out the Nielsen-Thurston category of floor homeomorphisms. subject matters contain the topology of the moduli house of Riemann surfaces, the relationship with floor bundles, pseudo-Anosov conception, and Thurston's method of the classification.
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