Parallel Transport over Path Spaces

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.

27pp 3fig pdflatex only; v2: rewritten with several clarifications; v3: minor changes, added references. Version to be published, 30pp

Cited by in corpus (7)

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• On higher holonomy invariants in higher gauge theory I
• On the global $2$-holonomy for a $2$-connection on a $2$-bundle
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• On 2-Holonomy
• Geometric prequantization on the path space of a prequantized manifold
• Geodesics on path spaces and double category