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Vector Bundles from an Algebraic Viewpoint

Gunjal, Milind Vishwas (2019) Vector Bundles from an Algebraic Viewpoint. Masters thesis, Indian Institute of Science Education and Research Kolkata.

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    Abstract

    In this thesis, we will give a brief introduction to projective modules and vector bundles and discuss the correspondence between modules over the ring of continuous functions (C(X)) and vector bundles over X. We will also introduce covering space theory to get a better understanding of correspondence between algebraic and topological objects. A detailed discussion about the compactifications is also presented. We will also establish the notion of localization of vector bundles in terms of localization of C(X)-modules at a point using Swan’s theorem. We will discuss some examples of Swan’s theorem. Finally, we motivate the statement of the Quillen-Suslin theorem.

    Item Type: Thesis (Masters)
    Additional Information: Supervisor: Dr. Somnath Basu
    Uncontrolled Keywords: Compactification; Double Covers; Finitely Generated Projective C(X)-modules; Localization; Vector Bundles
    Subjects: Q Science > QC Physics
    Divisions: Department of Mathematics and Statistics
    Depositing User: IISER Kolkata Librarian
    Date Deposited: 14 Oct 2019 13:04
    Last Modified: 14 Oct 2019 13:05
    URI: http://eprints.iiserkol.ac.in/id/eprint/879

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