Parallel Transport over Path Spaces
Saikat Chatterjee, Amitabha Lahiri, Ambar N. Sengupta
TL;DR
This paper introduces a differential geometric framework for parallel transport over path spaces, combining continuum and discrete theories within a category-theoretic approach to enhance understanding of geometric transport phenomena.
Contribution
It presents a novel integrated framework for parallel transport over path spaces, bridging continuum and discrete theories using category theory.
Findings
Unified geometric framework developed
Discrete and continuum theories integrated
Potential applications in advanced geometric analysis
Abstract
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.
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