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Rational Structures and Fractional Differential Refinements

Wheeler, Matthew (2016) Rational Structures and Fractional Differential Refinements. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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In the following thesis, we explore the notion of rational Fivebrane structures. This is done through a combination of obstruction theory and rational homotopy theory. We show that these structures can be classified to some degree by the underlying Spin bundle. From there we turn our focus to the differential setting. Using this relation to the Spin bundle, we apply the classical machinery of Cheeger and Simons to understand differential rational Fivebrane classes. Finally we use these classes to obtain information for differential trivializations in the integral case. In doing this we introduce the exact braid diagram.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Wheeler, Matthewmaw148@pitt.eduMAW148
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairSati, Hishamhsati@pitt.eduHSATI
Committee MemberGartside, Paul
Committee MemberDeblois, Jason
Committee MemberRedden, Corbett
Date: 3 October 2016
Date Type: Publication
Defense Date: 14 June 2016
Approval Date: 3 October 2016
Submission Date: 27 July 2016
Access Restriction: 2 year -- Restrict access to University of Pittsburgh for a period of 2 years.
Number of Pages: 113
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: string and fivebrane structures, rational homotopy theory, differential cohomology, differential braid diagram, fractional differential characters
Date Deposited: 03 Oct 2016 20:27
Last Modified: 03 Oct 2018 05:15


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