Mathematics, Volume 12, Issue 13 (July-1 2024) – 227 articles
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The theory of fiber bundles forms a fundamental and versatile basis for many applications in mathematics and physics. A special class are the principal bundles, where the fiber is a torsor—a free group-space homeomorphic to the group. Inspired by adiabatic quantum mechanics, this work considers group-spaces where the fibers are generalized to disjoint unions of torsors, called semi-torsors, which then form semi-principal bundles. These extend the principal bundles, and similarly support equivariant parallel transport. The main difference is that this parallel transport may now end up in a different group orbit, meaning that group translations can no longer describe the situation. This can be mediated by introducing frames of group-spaces, which supply the needed reference points and enable the passage to a (principal) frame bundle. View this paper
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