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Barcode Structure of Persistence Modules via Local Structure

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2020, Master of Science, Ohio State University, Mathematics.
We present a generalization of a d-dimensional zigzag module called a C-module, which is a functor M : C → (V ect/k). To study C-modules we present notions of multiflags, general position of multiflags and modules, the associated graded of a multiflag, and the local structure of a module. We present a theorem of C. Ogle in [5] describing when a module decomposes as a direct sum of blocks. We also show how to construct sums, products, and tensors of modules, and give a Kunneth Theorem for Local Structure. We show that any multiflag where every subspace covers at most 2 subspaces is in general position. We also show that general position is equivalent to the existence a special type of basis. We use these results to provide another proof that persistence modules decompose as a direct sum of interval submodules.
Crichton Ogle, Dr. (Advisor)
Sanjeevi Krishnan, Dr. (Committee Member)
51 p.

Recommended Citations

Citations

  • Sultan, S. A. (2020). Barcode Structure of Persistence Modules via Local Structure [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1587648185552845

    APA Style (7th edition)

  • Sultan, Sami. Barcode Structure of Persistence Modules via Local Structure. 2020. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1587648185552845.

    MLA Style (8th edition)

  • Sultan, Sami. "Barcode Structure of Persistence Modules via Local Structure." Master's thesis, Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1587648185552845

    Chicago Manual of Style (17th edition)