{"product_id":"a-primer-on-mapping-class-groups-9780691147949","title":"A Primer on Mapping Class Groups (Pms-49)","description":"\u003cp\u003eThe study of the mapping class group Mod(\u003ci\u003eS\u003c\/i\u003e) 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. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e \u003ci\u003eA Primer on Mapping Class Groups\u003c\/i\u003e begins by explaining the main group-theoretical properties of Mod(\u003ci\u003eS\u003c\/i\u003e), 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 Teichm?ller space and its geometry, and uses the action of Mod(\u003ci\u003eS\u003c\/i\u003e) 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.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAbout the Author\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eBenson Farb\u003c\/b\u003e is professor of mathematics at the University of Chicago. He is the editor of \u003ci\u003eProblems on Mapping Class Groups and Related Topics\u003c\/i\u003e and the coauthor of \u003ci\u003eNoncommutative Algebra\u003c\/i\u003e. \u003cb\u003eDan Margalit\u003c\/b\u003e is assistant professor of mathematics at Georgia Institute of Technology.\u003cbr\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":50412814631186,"sku":"9780691147949","price":108.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0831\/4771\/8930\/files\/img_2356a329-a377-40cb-997b-7ef806041f08.jpg?v=1729330107","url":"https:\/\/surprise-castle.myshopify.com\/products\/a-primer-on-mapping-class-groups-9780691147949","provider":"Surprise Castle","version":"1.0","type":"link"}