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Superconnections and Parallel Transport

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posted on 2006-07-21, 00:00 authored by Florin Dumitrescu
We construct a notion of parallel transport along superpaths in a manifold that corresponds to a superconnection (`{a} la Quillen), in an attempt to understand geometrically superconnections, the same way as an appropriate notion of parallel transport along paths translates geometrically the concept of a connection. The parallel transport along superpaths is realized by solving some ``half-order' differential equations, as opposed to solving first-order differential equations for the usual parallel transport. Before doing this, we extend the usual notion of parallel transport along paths associated to a connection to superpaths, and see how the super-parallel transport incorporates the analytical concept of a connection. Such considerations are motivated by trying to understand one dimensional supersymmetric field theories over a manifold, in the hope that they provide geometric cocycles for differential K-theory. The larger context is the Stolz-Teichner program (see cite{ST}) of relating field theories and cohomology theories, and our effort is to complete the understanding of the one-dimensional story.

History

Date Modified

2017-06-02

Defense Date

2006-06-30

Research Director(s)

Stephan Stolz

Committee Members

Stephan Stolz

Degree

  • Doctor of Philosophy

Degree Level

  • Doctoral Dissertation

Language

  • English

Alternate Identifier

etd-07212006-131339

Publisher

University of Notre Dame

Additional Groups

  • Mathematics

Program Name

  • Mathematics

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