|
|
Type of Document Dissertation Author Dumitrescu, Florin URN etd-07212006-131339 Title Superconnections and Parallel Transport Degree Doctor of Philosophy Department Mathematics Advisory Committee
Advisor Name Title Stephan Stolz Committee Member Keywords
- field theories
Date of Defense 2006-06-30 Availability unrestricted Abstract We construct a notion of parallel transport along superpaths in amanifold 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.
Files
Filename Size Approximate Download Time (Hours:Minutes:Seconds)
28.8 Modem 56K Modem ISDN (64 Kb) ISDN (128 Kb) Higher-speed Access DumitrescuF062006.pdf 502.90 Kb 00:02:19 00:01:11 00:01:02 00:00:31 00:00:02