Connections on decorated path space bundles. (English) Zbl 1355.53018
Summary: For a principal bundle \(P \rightarrow M\) equipped with a connection \(\overline{A}\), we study an infinite dimensional bundle \(\mathcal{P}_{\overline{A}}^{\operatorname{dec}} P\) over the space of paths on \(M\), with the points of \(\mathcal{P}_{\overline{A}}^{\operatorname{dec}} P\) being horizontal paths on \(P\) decorated with elements of a second structure group. We construct parallel transport processes on such bundles and study holonomy bundles in this setting.
MSC:
| 53C05 | Connections (general theory) |
| 18F15 | Abstract manifolds and fiber bundles (category-theoretic aspects) |
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