By Benson Farb
The examine of the mapping classification crew Mod(S) is a classical subject that's experiencing a renaissance. It lies on the juncture of geometry, topology, and staff conception. This publication explains as many vital theorems, examples, and strategies as attainable, speedy and without delay, whereas even as giving complete information and conserving the textual content approximately self-contained. The booklet is appropriate for graduate students.
A Primer on Mapping category Groups starts by way of explaining the most group-theoretical houses of Mod(S), from finite iteration via Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. alongside the way in which, valuable gadgets and instruments are brought, reminiscent of the Birman specified series, the complicated of curves, the braid workforce, the symplectic illustration, and the Torelli crew. 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 class of floor homeomorphisms. themes comprise the topology of the moduli area of Riemann surfaces, the relationship with floor bundles, pseudo-Anosov thought, and Thurston's method of the classification.
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