By Benson Farb,Dan Margalit
The learn of the mapping category workforce Mod(S) is a classical subject that's experiencing a renaissance. It lies on the juncture of geometry, topology, and team thought. This e-book explains as many very important theorems, examples, and strategies as attainable, quick and at once, whereas while giving complete information and retaining the textual content approximately self-contained. The booklet is acceptable for graduate students.
A Primer on Mapping category Groups starts through explaining the most group-theoretical homes of Mod(S), from finite iteration by way of Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. alongside the best way, vital gadgets and instruments are brought, akin to the Birman certain series, the complicated of curves, the braid crew, the symplectic illustration, and the Torelli staff. The ebook then introduces Teichmüller area and its geometry, and makes use of the motion of Mod(S) on it to end up 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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Extra info for A Primer on Mapping Class Groups (PMS-49) (Princeton Mathematical Series)
A Primer on Mapping Class Groups (PMS-49) (Princeton Mathematical Series) by Benson Farb,Dan Margalit