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  1. Bog
  2. Geometri
  3. Algebraisk geometri

A Primer on Mapping Class Groups

Af: Dan Margalit, Benson Farb Engelsk Hardback

A Primer on Mapping Class Groups

Af: Dan Margalit, Benson Farb Engelsk Hardback
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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.

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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.

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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 488
ISBN-13: 9780691147949
Indbinding: Hardback
Udgave:
ISBN-10: 0691147949
Kategori: Algebraisk geometri
Udg. Dato: 16 okt 2011
Længde: 37mm
Bredde: 165mm
Højde: 239mm
Forlag: Princeton University Press
Oplagsdato: 16 okt 2011
Forfatter(e): Dan Margalit, Benson Farb
Forfatter(e) Dan Margalit, Benson Farb

Kategori Algebraisk geometri

ISBN-13 9780691147949

Sprog Engelsk

Indbinding Hardback

Sider 488

Udgave

Længde 37mm

Bredde 165mm

Højde 239mm

Udg. Dato 16 okt 2011

Oplagsdato 16 okt 2011

Forlag Princeton University Press

Kategori sammenhænge