2013/09/10 by Vincent S. Schlegel, Schlegel, Vincent S.
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #hep-th #math.DG
paper · pdf · doi:10.48550/arxiv.1309.2601
Master of Philosophy thesis
arxiv created 2013/09/10 · openalex publication_date 2013/09/10 · arxiv updated 2013/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The caloron correspondence is a tool that gives an equivalence between principal G-bundles based over the manifold M × S1 and principal LG-bundles on M, where LG is the Fréchet Lie group of smooth loops in the Lie group G. This thesis uses the caloron correspondence to construct certain differential forms called "string potentials" that play the same role as Chern-Simons forms for loop group bundles. Following their construction, the string potentials are used to define degree 1 differential characteristic classes for ΩU(n)-bundles. The notion of an "Ω vector bundle" is introduced and a caloron correspondence is developed for these objects. Finally, string potentials and Ω vector bundles are used to define an Ω bundle version of the structured vector bundles of Simons--Sullivan. The "Ω model" of odd differential K-theory is constructed using these objects and an elementary differential extension of odd K-theory due to Tradler et al.