By Benson Farb,Dan Margalit
The research of the mapping category staff Mod(S) is a classical subject that's experiencing a renaissance. It lies on the juncture of geometry, topology, and workforce thought. This publication explains as many very important theorems, examples, and strategies as attainable, fast and at once, whereas while giving complete information and protecting the textual content approximately self-contained. The e-book is appropriate for graduate students.
A Primer on Mapping classification Groups starts via explaining the most group-theoretical houses of Mod(S), from finite new release by means of Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. alongside the best way, important gadgets and instruments are brought, reminiscent of the Birman distinct series, the advanced of curves, the braid staff, the symplectic illustration, and the Torelli team. 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 type 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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