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Full-Text Articles in Physical Sciences and Mathematics
Representing The Derivative Of Trace Of Holonomy, Jeffrey Peter Kroll
Representing The Derivative Of Trace Of Holonomy, Jeffrey Peter Kroll
Dissertations, Theses, and Capstone Projects
Trace of holonomy around a fixed loop defines a function on the space of unitary connections on a hermitian vector bundle over a Riemannian manifold. Using the derivative of trace of holonomy, the loop, and a flat unitary connection, a functional is defined on the vector space of twisted degree 1 cohomology classes with coefficients in skew-hermitian bundle endomorphisms. It is shown that this functional is obtained by pairing elements of cohomology with a degree 1 homology class built directly from the loop and equipped with a flat section obtained from the variation of holonomy around the loop. When the …
A Geometric Model For Real And Complex Differential K-Theory, Matthew T. Cushman
A Geometric Model For Real And Complex Differential K-Theory, Matthew T. Cushman
Dissertations, Theses, and Capstone Projects
We construct a differential-geometric model for real and complex differential K-theory based on a smooth manifold model for the K-theory spectra defined by Behrens using spaces of Clifford module extensions. After writing representative differential forms for the universal Pontryagin and Chern characters we transgress these forms to all the spaces of the spectra and use them to define an abelian group structure on maps up to an equivalence relation that refines homotopy. Finally we define the differential K-theory functors and verify the axioms of Bunke-Schick for a differential cohomology theory.