Definable G vector bundles over a definable G set with free action

Key Points

• The aim is to establish a one-to-one correspondence between isomorphism classes of definable G vector bundles and definable vector bundles over a quotient set.
• Definition of definable G vector bundles and characterizing their properties.
• Analysis of free actions on definable G sets.
• Establishment of a bijection correlating the classes of bundles.
• Proven correspondence between isomorphism classes of definable G vector bundles and definable bundles over X/G.
• Demonstrated the consistency of the correspondence under free action conditions.