• About
    • Login
    View Item 
    •   Institutional Repository Home
    • Electronic Theses and Dissertations
    • Electronic Theses and Dissertations
    • View Item
    •   Institutional Repository Home
    • Electronic Theses and Dissertations
    • Electronic Theses and Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of Institutional RepositoryCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsDepartmentThis CollectionBy Issue DateAuthorsTitlesSubjectsDepartment

    My Account

    LoginRegister

    On the Classification of Closed Flat Four-Manifolds

    Lambert, Thomas Paul
    : https://etd.library.vanderbilt.edu/etd-07252007-095611
    http://hdl.handle.net/1803/13562
    : 2007-07-31

    Abstract

    In this thesis, we discuss the classification of closed flat four-manifolds. First, we give a brief treatment of the history of this problem, with a discussion of the advantages, disadvantages, and inconsistencies among the previous classifications. Then, we discuss the process by which we reconcile the different classifications. The procedure is to exhibit presentations as isometry groups of the 74 groups corresponding to the manifolds. We determine fiber-bundle or twisted $I$-bundle decompositions of the manifolds, along with their homology and holonomy groups. Also, we determine the orientable double-covers for the nonorientable manifolds. In addition, we match our list of manifolds to those of the previous primary sources.
    Show full item record

    Files in this item

    Icon
    Name:
    phdthesis.pdf
    Size:
    376.9Kb
    Format:
    PDF
    View/Open

    This item appears in the following collection(s):

    • Electronic Theses and Dissertations

    Connect with Vanderbilt Libraries

    Your Vanderbilt

    • Alumni
    • Current Students
    • Faculty & Staff
    • International Students
    • Media
    • Parents & Family
    • Prospective Students
    • Researchers
    • Sports Fans
    • Visitors & Neighbors

    Support the Jean and Alexander Heard Libraries

    Support the Library...Give Now

    Gifts to the Libraries support the learning and research needs of the entire Vanderbilt community. Learn more about giving to the Libraries.

    Become a Friend of the Libraries

    Quick Links

    • Hours
    • About
    • Employment
    • Staff Directory
    • Accessibility Services
    • Contact
    • Vanderbilt Home
    • Privacy Policy