Parallel Transport over Path Spaces
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We develop a differential geometric framework for parallel transport over path spaces and a corresponding discrete theory, an integrated version of the continuum theory, using a category-theoretic framework.
💡 Research Summary
The paper “Parallel Transport over Path Spaces” develops a comprehensive geometric and categorical framework for defining parallel transport not on points of a manifold but on the space of smooth paths within that manifold. The authors begin by endowing the path space (P M) (the collection of all smooth curves (\gamma:
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