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Thesis.pdf (316.34 KB)
ETD Abstract Container
Abstract Header
Barcode Structure of Persistence Modules via Local Structure
Author Info
Sultan, Sami A
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1587648185552845
Abstract Details
Year and Degree
2020, Master of Science, Ohio State University, Mathematics.
Abstract
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.
Committee
Crichton Ogle, Dr. (Advisor)
Sanjeevi Krishnan, Dr. (Committee Member)
Pages
51 p.
Subject Headings
Mathematics
Keywords
TDA
;
persistence module
;
zigzag module
;
local structure
;
general position
;
barcode
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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)
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Document number:
osu1587648185552845
Download Count:
177
Copyright Info
© 2020, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.