By Benson Farb
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 team conception. This e-book explains as many vital theorems, examples, and strategies as attainable, fast and at once, whereas even as giving complete info and preserving the textual content approximately self-contained. The publication is appropriate for graduate students.
A Primer on Mapping classification Groups starts off through 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, imperative items and instruments are brought, equivalent to the Birman specific series, the advanced of curves, the braid team, the symplectic illustration, and the Torelli team. The ebook then introduces Teichmüller house and its geometry, and makes use of the motion of Mod(S) on it to turn out the Nielsen-Thurston class 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.
Read or Download A Primer on Mapping Class Groups (PMS-49) (Princeton Mathematical Series) PDF
Best Abstract books
The current variation differs from the 1st in different locations. specifically our remedy of polycyclic and in the community polycyclic groups-the such a lot typical generalizations of the classical proposal of a finite soluble group-has been multiplied. We thank Ju. M. Gorcakov, V. A. Curkin and V. P. Sunkov for lots of worthy feedback.
This article is meant to function an creation to the geometry of the motion of discrete teams of Mobius variations. the subject material has now been studied with altering issues of emphasis for over 100 years, the newest advancements being hooked up with the speculation of 3-manifolds: see, for instance, the papers of Poincare  and Thurston .
Homological algebra has discovered quite a few purposes in lots of fields starting from finite and countless workforce conception to illustration concept, quantity conception, algebraic topology and sheaf concept. within the re-creation of this vast creation to the sphere, the authors deal with a few opt for issues and describe their purposes, illustrating the diversity and intensity in their advancements.
Fourier research is an integral instrument for physicists, engineers and mathematicians. a wide selection of the concepts and purposes of fourier research are mentioned in Dr. Körner's hugely well known publication, An creation to Fourier research (1988). during this e-book, Dr. Körner has compiled a set of workouts on Fourier research that would completely try the reader's figuring out of the topic.
Additional info for A Primer on Mapping Class Groups (PMS-49) (Princeton Mathematical Series)