Obstructions to realizing mapping classes by diffeomorphisms /

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Bibliographic Details
Author / Creator:Tshishiku, Bena, author.
Imprint:2015.
Ann Arbor : ProQuest Dissertations & Theses, 2015
Description:1 electronic resource (115 pages)
Language:English
Format: E-Resource Dissertations
Local Note:School code: 0330
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/10773179
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Other authors / contributors:University of Chicago. degree granting institution.
ISBN:9781321914924
Notes:Advisors: Benson Farb Committee members: Danny Calegari.
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Dissertation Abstracts International, Volume: 76-12(E), Section: B.
English
Summary:For a based manifold M, *, the question of whether the surjective homomorphism Diff(M, *) → π0 Diff(M, *)$ admits a section is an example of a Nielsen realization problem. This question is related to a question about flat connections on M -bundles and is meaningful for M of any dimension. In dimension 2, Bestvina-Church-Souto showed a section does not exist when M is closed and has genus g ≥ 2. Their techniques are cohomological and certain aspects are specific to surfaces. We exhibit new cohomological obstructions to the existence of a section σ: π 0 Diff(M, *) → Diff(M, *). The main tools include Chern-Weil theory, Milnor-Wood inequalities, and Margulis superrigidity. For a large class of locally symmetric manifolds M = Γ\ G/K, we show that σ does not exist by showing that our obstructions are nonvanishing. For many M, this reduces to showing that M has some Pontryagin class pi ( M ) that is nonzero. We compute low degree Pontryagin classes for every closed locally symmetric manifold of noncompact type, building off an algorithm developed by Borel-Hirzebruch. As a result of our computation, we answer the question: Which closed locally symmetric M have at least one nonzero Pontryagin class?