By Benson Farb
The examine of the mapping classification workforce Mod(S) is a classical subject that's experiencing a renaissance. It lies on the juncture of geometry, topology, and staff idea. This ebook explains as many vital theorems, examples, and strategies as attainable, fast and without delay, whereas even as giving complete info and maintaining the textual content approximately self-contained. The e-book is acceptable for graduate students.
A Primer on Mapping type Groups starts via explaining the most group-theoretical houses of Mod(S), from finite new release through 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 distinctive series, the complicated of curves, the braid team, the symplectic illustration, and the Torelli staff. The e-book then introduces Teichmüller area and its geometry, and makes use of the motion of Mod(S) on it to turn out the Nielsen-Thurston category of floor homeomorphisms. themes contain the topology of the moduli area of Riemann surfaces, the relationship with floor bundles, pseudo-Anosov idea, and Thurston's method of the classification.
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