A Primer on Mapping Class Groups (PMS-49)

Nonfiction, Science & Nature, Mathematics, Topology, Geometry
Cover of the book A Primer on Mapping Class Groups (PMS-49) by Benson Farb, Dan Margalit, Princeton University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Benson Farb, Dan Margalit ISBN: 9781400839049
Publisher: Princeton University Press Publication: September 26, 2011
Imprint: Princeton University Press Language: English
Author: Benson Farb, Dan Margalit
ISBN: 9781400839049
Publisher: Princeton University Press
Publication: September 26, 2011
Imprint: Princeton University Press
Language: English

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students.

A Primer on Mapping Class Groups begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students.

A Primer on Mapping Class Groups begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.

More books from Princeton University Press

Cover of the book The Language of Global Success by Benson Farb, Dan Margalit
Cover of the book The Computer from Pascal to von Neumann by Benson Farb, Dan Margalit
Cover of the book Wild Profusion by Benson Farb, Dan Margalit
Cover of the book The Sun's Influence on Climate by Benson Farb, Dan Margalit
Cover of the book Birds of New Guinea by Benson Farb, Dan Margalit
Cover of the book The Global Remapping of American Literature by Benson Farb, Dan Margalit
Cover of the book Kierkegaard's Writings, XVI: Works of Love by Benson Farb, Dan Margalit
Cover of the book Uncouth Nation by Benson Farb, Dan Margalit
Cover of the book Proving Woman by Benson Farb, Dan Margalit
Cover of the book Physicalism, or Something Near Enough by Benson Farb, Dan Margalit
Cover of the book Faith in Schools? by Benson Farb, Dan Margalit
Cover of the book Egypt after Mubarak by Benson Farb, Dan Margalit
Cover of the book The Agony of the Russian Idea by Benson Farb, Dan Margalit
Cover of the book Humanity by Benson Farb, Dan Margalit
Cover of the book Impossible? by Benson Farb, Dan Margalit
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy