Download E-books A Primer on Mapping Class Groups (PMS-49) (Princeton Mathematical Series) PDF

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.

Show description

Read or Download A Primer on Mapping Class Groups (PMS-49) (Princeton Mathematical Series) PDF

Best Abstract books

Introduction to Local Spectral Theory

Glossy neighborhood spectral thought is outfitted at the classical spectral theorem, a basic bring about single-operator concept and Hilbert areas. This booklet presents an in-depth advent to the average growth of this attention-grabbing subject of Banach house operator concept. It offers whole insurance of the sector, together with the basic fresh paintings via Albrecht and Eschmeier which supplies the total duality conception for Banach house operators.

More Concise Algebraic Topology: Localization, Completion, and Model Categories (Chicago Lectures in Mathematics)

With company foundations courting in basic terms from the Fifties, algebraic topology is a comparatively younger sector of arithmetic. There are only a few textbooks that deal with basic subject matters past a primary path, and lots of issues now necessary to the sphere are usually not handled in any textbook. J. Peter May’s A Concise direction in Algebraic Topology addresses the traditional first path fabric, comparable to primary teams, masking areas, the fundamentals of homotopy concept, and homology and cohomology.

Lie Groups: An Approach through Invariants and Representations (Universitext)

Lie teams has been an expanding zone of concentration and wealthy examine because the heart of the twentieth century. In Lie teams: An procedure via Invariants and Representations, the author's masterful technique supplies the reader a complete therapy of the classical Lie groups besides an intensive advent to quite a lot of themes linked to Lie teams: symmetric capabilities, thought of algebraic types, Lie algebras, tensor algebra and symmetry, semisimple Lie algebras, algebraic teams, workforce representations, invariants, Hilbert conception, and binary varieties with fields starting from natural algebra to sensible research.

Topological Methods in Group Theory (Graduate Texts in Mathematics)

This publication is ready the interaction among algebraic topology and the idea of countless discrete teams. it's a highly very important contribution to the sphere of topological and geometric team conception, and is certain to turn into a regular reference within the box. to maintain the size average and the focal point transparent, the writer assumes the reader understands or can simply examine the required algebra, yet desires to see the topology performed intimately.

Additional resources for A Primer on Mapping Class Groups (PMS-49) (Princeton Mathematical Series)

Show sample text content

Rated 4.96 of 5 – based on 24 votes