The Topology of Surface Bundles: Cohomology and Enumerations of Fiberings /

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Bibliographic Details
Author / Creator:Salter, Nicholas, author.
Ann Arbor : ProQuest Dissertations & Theses, 2017
Description:1 electronic resource (91 pages)
Format: E-Resource Dissertations
Local Note:School code: 0330
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Other authors / contributors:University of Chicago. degree granting institution.
Notes:Advisors: Benson Farb Committee members: Danny Calegari.
Dissertation Abstracts International, Volume: 78-12(E), Section: B.
Summary:This thesis undertakes a study of surface bundles, especially 4-manifolds equipped with one or more surface bundle structures. A central theme is the interplay between the number of surface bundle structures on a manifold, the properties of the associated monodromy representations, and the algebro-topological invariants of the manifold. In Chapter 1, we show that any non-trivial surface bundle with monodromy in the Johnson kernel has a unique fibering. In Chapter 2, we provide the first examples of 4-manifolds admitting 3 or more surface bundle structures. In Chapter 3, we study how the cohomology algebra of a surface bundle can be computed from the monodromy representation, and relate this problem to the cohomology of the mapping class group and the Torelli subgroup.