Smooth Stratified Vector Bundles and Obstructions to Their Orthonormal Frame Bundles

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dc.contributor.authorScarlett, Varun Kheren
dc.contributor.committeechairHaskell, Peter E.en
dc.contributor.committeememberMihalcea, Constantin Leonardoen
dc.contributor.committeememberSchultz, Michael Thomasen
dc.contributor.committeememberYang, Yunen
dc.contributor.departmentMathematicsen
dc.date.accessioned2023-05-24T08:00:30Zen
dc.date.available2023-05-24T08:00:30Zen
dc.date.issued2023-05-23en
dc.description.abstractMotivated by the example of the tangent bundle of a stratified space, which is no longer a vector bundle, we begin the construction of a general theory of smooth stratified vector bundles. We show that one can construct a frame bundle of a smooth stratified vector bundle in a canonical way, but that there are substantial obstructions to constructing an orthonormal frame bundle.en
dc.description.abstractgeneralSmooth manifolds are the natural class of spaces on which we can perform the normal operations of calculus. There have been many efforts to generalize the class of spaces on which one can perform these operations. One possible class are stratified spaces, which are spaces that are built out of smooth manifolds in sufficiently nice ways. Spaces such as vector bundles and their frame bundles play a central role in the smooth manifold theory, and here we begin the development of the appropriate corresponding theory for stratified spaces.en
dc.description.degreeMaster of Scienceen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:37924en
dc.identifier.urihttp://hdl.handle.net/10919/115162en
dc.language.isoenen
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectStratified Vector Bundlesen
dc.subjectStratified Frame Bundlesen
dc.subjectDifferential Geometryen
dc.titleSmooth Stratified Vector Bundles and Obstructions to Their Orthonormal Frame Bundlesen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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