By Benson Farb,Dan Margalit
The examine 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 concept. This booklet explains as many vital theorems, examples, and strategies as attainable, fast and at once, whereas even as giving complete info and retaining the textual content approximately self-contained. The booklet is acceptable for graduate students.
A Primer on Mapping classification Groups starts off through explaining the most group-theoretical homes 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, significant gadgets and instruments are brought, reminiscent of the Birman detailed series, the complicated of curves, the braid crew, the symplectic illustration, and the Torelli workforce. The booklet then introduces Teichmüller house and its geometry, and makes use of the motion of Mod(S) on it to turn out the Nielsen-Thurston category of floor homeomorphisms. issues comprise 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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