Parallel transport over path spaces. (English) Zbl 1208.81107

The authors develop both a path-space geometric theory and a category theoretic approach to surface holonomy, and describe the relationships between the two.


81Q70 Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory
81T13 Yang-Mills and other gauge theories in quantum field theory
58Z05 Applications of global analysis to the sciences
16E45 Differential graded algebras and applications (associative algebraic aspects)
Full Text: DOI arXiv


[1] DOI: 10.1007/s002200050655 · Zbl 0939.58009
[2] DOI: 10.1090/S0002-9947-1971-0275312-1
[3] DOI: 10.2307/1970846 · Zbl 0227.58003
[4] Ehresmann C., Ann. Sci. École Norm. Sup. 80 pp 349– · Zbl 0128.02002
[5] Ehresmann C., Catégories et structures (1965)
[6] DOI: 10.1063/1.1790048 · Zbl 1071.53011
[7] DOI: 10.1142/S0219887804000186 · Zbl 1081.53045
[8] DOI: 10.1112/jlms/54.2.403 · Zbl 0867.55019
[9] DOI: 10.1016/S0003-4916(03)00147-7 · Zbl 1056.70013
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.