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This thesis analyzes topological aspects of infinite rank bundles with gauge groups and invertible pseudodifferential operators as transition maps. These bundles appear naturally in infinite dimensional geometry, for instance, when studying the geometry of mapping spaces between closed manifolds. In the first part, using an analogue of Chern-Weil theory, we construct characteristic classes for these bundles (called exotic characteristic classes) and use them to find topologically nontrivial examples. In particular, we construct nonzero elements in the cohomology of a mapping space. In the second part, we define a K-theory ring for psendodifferential bundles and use exotic classes to find nonzero elements in this ring.
Thesis (Ph.D.)--Boston UniversityPLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at firstname.lastname@example.org. Thank you.