Wheeler, Matthew
(2016)
Rational Structures and Fractional Differential Refinements.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
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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Details
Item Type: |
University of Pittsburgh ETD
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Status: |
Unpublished |
Creators/Authors: |
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ETD Committee: |
Title | Member | Email Address | Pitt Username | ORCID |
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Committee Chair | Sati, Hisham | hsati@pitt.edu | HSATI | | Committee Member | Gartside, Paul | | | | Committee Member | Deblois, Jason | | | | Committee Member | Redden, Corbett | | | |
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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 |
URI: |
http://d-scholarship.pitt.edu/id/eprint/28594 |
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