Scarlett, Varun Kher2023-05-242023-05-242023-05-23vt_gsexam:37924http://hdl.handle.net/10919/115162Motivated 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.ETDenIn CopyrightStratified Vector BundlesStratified Frame BundlesDifferential GeometryThesis