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Wayne State University

1. Zabka, Matthew John. Cohomology Operations On Random Spaces.

Degree: PhD, Mathematics, 2016, Wayne State University

Topology has recently received more attention from statisticians as some its tools have been applied to understanding the shape of data. In particular, a data set can generate a topological space, and this space’s topological structure can give us insight into some properties of the data. This framework has made it necessary to study random spaces generated by data. For example, without an understanding of the probabilistic properties of random spaces, one cannot conclude with any degree of confidence what the tools of topology tell us about a data set. While some results are known about the cohomological structure of a random space, not much is known about how cohomology operations behave on random spaces. This dissertation proves some results about the asymptotic properties of cohomology operations on random spaces and discusses the idea of a random Bockstein operation in a related purely algebraic context. Advisors/Committee Members: Daniel C. Isaksen.

Subjects/Keywords: Bockstein; Cohomology operations; Mathematics; Statistics and Probability

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Zabka, M. J. (2016). Cohomology Operations On Random Spaces. (Doctoral Dissertation). Wayne State University. Retrieved from https://digitalcommons.wayne.edu/oa_dissertations/1500

Chicago Manual of Style (16th Edition):

Zabka, Matthew John. “Cohomology Operations On Random Spaces.” 2016. Doctoral Dissertation, Wayne State University. Accessed October 28, 2020. https://digitalcommons.wayne.edu/oa_dissertations/1500.

MLA Handbook (7th Edition):

Zabka, Matthew John. “Cohomology Operations On Random Spaces.” 2016. Web. 28 Oct 2020.

Vancouver:

Zabka MJ. Cohomology Operations On Random Spaces. [Internet] [Doctoral dissertation]. Wayne State University; 2016. [cited 2020 Oct 28]. Available from: https://digitalcommons.wayne.edu/oa_dissertations/1500.

Council of Science Editors:

Zabka MJ. Cohomology Operations On Random Spaces. [Doctoral Dissertation]. Wayne State University; 2016. Available from: https://digitalcommons.wayne.edu/oa_dissertations/1500

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