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A primer on mapping class groups /

Farb, Benson.

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A primer on mapping class groups /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	A primer on mapping class groups // Benson Farb and Dan Margalit.
作者:	Farb, Benson.
其他作者:	Margalit, Dan,
出版者:	Princeton, NJ :Princeton University Press, : c2012.,
面頁冊數:	xiv, 472 p. :ill. ;25 cm.
標題:	Mappings (Mathematics) -
ISBN:	9780691147949 (hbk.) :

A primer on mapping class groups /
Farb, Benson.

A primer on mapping class groups /Benson Farb and Dan Margalit. - Princeton, NJ :Princeton University Press,c2012. - xiv, 472 p. :ill. ;25 cm. - Princeton mathematical series.

Includes bibliographical references (p. [447]-463) and index.

"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.The book 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 Teichm羹ller 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"--

ISBN: 9780691147949 (hbk.) :US75.00

LCCN: 2011008491Subjects--Topical Terms:

662203
Mappings (Mathematics)

LC Class. No.: QA360 / .F37 2012

Dewey Class. No.: 512.7/4

A primer on mapping class groups /
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245 1 0 $a A primer on mapping class groups / $c Benson Farb and Dan Margalit.
260 # $a Princeton, NJ : $b Princeton University Press, $c c2012.
300 $a xiv, 472 p. : $b ill. ; $c 25 cm.
490 1 0 $a Princeton mathematical series
504 $a Includes bibliographical references (p. [447]-463) and index.
520 # $a "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.The book 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 Teichm羹ller 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"-- $c Provided by publisher.
650 # 0 $a Mappings (Mathematics) $3 662203
650 # 0 $a Class groups (Mathematics) $3 726458
650 # 7 $a MATHEMATICS / Advanced $2 bisacsh. $3 1535957
650 # 7 $a MATHEMATICS / Topology $2 bisacsh. $3 1535958
650 # 7 $a MATHEMATICS / Geometry / Algebraic $2 bisacsh. $3 1535959
700 1 # $a Margalit, Dan, $d 1976- $3 1535956