Surface Bundles

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. It 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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CHARACTERISTIC CLASSES OF SURFACE BUNDLES AND BOUNDED COHOMOLOGY

A Fête of Topology ◽

10.1016/b978-0-12-480440-1.50016-2 ◽

1988 ◽

pp. 233-257 ◽

Cited By ~ 5

Author(s):

S. Morita

Keyword(s):

Characteristic Classes ◽

Bounded Cohomology ◽

Surface Bundles

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On hyperbolic surface bundles over the circle as branched double covers of the $3$-sphere

Proceedings of the American Mathematical Society ◽

10.1090/proc/14825 ◽

2020 ◽

Vol 148 (4) ◽

pp. 1805-1814

Author(s):

Susumu Hirose ◽

Eiko Kin

Keyword(s):

Hyperbolic Surface ◽

Double Covers ◽

Surface Bundles

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When closed graph manifolds are finitely covered by surface bundles over S 1

Acta Mathematica Sinica English Series ◽

10.1007/s10114-999-0057-5 ◽

1999 ◽

Vol 15 (1) ◽

pp. 11-20 ◽

Cited By ~ 2

Author(s):

Yan Wang ◽

Fengchun Yu

Keyword(s):

Closed Graph ◽

Surface Bundles ◽

Graph Manifolds

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ON CLOSED LEAVES OF FOLIATIONS, MULTISECTIONS AND STABLE COMMUTATOR LENGTHS

Journal of Topology and Analysis ◽

10.1142/s1793525311000696 ◽

2011 ◽

Vol 03 (04) ◽

pp. 491-509

Author(s):

JONATHAN BOWDEN

Keyword(s):

Mapping Class Groups ◽

Mapping Class ◽

Intersection Numbers ◽

Class Groups ◽

Stable Mapping ◽

Surface Bundles

We give examples of foliations that answer two questions posed by Mitsumatsu and Vogt about the genus minimizing properties of closed leaves of 2-dimensional foliations on 4-manifolds. By studying stable commutator lengths in certain stable mapping class groups, we also answer an asymptotic version of another question of theirs concerning bounds on self-intersection numbers of multisections in surface bundles.

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