By Benson Farb,Dan Margalit
ISBN-10: 0691147949
ISBN-13: 9780691147949
The learn 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 crew concept. This booklet explains as many vital theorems, examples, and methods as attainable, speedy and without delay, whereas while giving complete information and preserving the textual content approximately self-contained. The booklet is appropriate for graduate students.
A Primer on Mapping classification Groups starts off by way of 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 best way, crucial gadgets and instruments are brought, resembling the Birman particular series, the advanced of curves, the braid crew, the symplectic illustration, and the Torelli workforce. The booklet then introduces Teichmüller area and its geometry, and makes use of the motion of Mod(S) on it to end up the Nielsen-Thurston type of floor homeomorphisms. themes contain the topology of the moduli area of Riemann surfaces, the relationship with floor bundles, pseudo-Anosov conception, 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
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