Smooth Stratified Vector Bundles and Obstructions to Their Orthonormal Frame Bundles

Motivated 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.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2023

Author dc:creator

• Scarlett, Varun Kher

Chair dc:contributor.committeechair

• Haskell, Peter E.

Committee members dc:contributor.committeemember

• Mihalcea, Constantin Leonardo
• Schultz, Michael Thomas
• Yang, Yun

• Stratified Vector Bundles
• Stratified Frame Bundles
• Differential Geometry

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

vt_gsexam:37924

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/115162