Free Lie algebroids and the space of paths
| dc.creator | Kapranov, Mikhail | |
| dc.date | 2007-02-20 | |
| dc.date | 2007-07-17 | |
| dc.date.accessioned | 2026-07-07T08:18:38Z | |
| dc.date.available | 2026-07-07T08:18:38Z | |
| dc.description | We construct algebraic and algebro-geometric models for the spaces of unparametrized paths. This is done by considering a path as a holonomy functional on indeterminate connections. For a manifold X, we construct a Lie algebroid P which serves as the tangent space to X (punctual paths) inside the space of all unparametrized paths. It serves as a natural receptacle of all "covariant derivatives of the curvature" for all bundles with connections on X. If X is an algebraic variety, we integrate P to a formal groupoid G which can be seen as the formal neighborhood of X inside the space of paths. We establish a relation of G with the stable map spaces of Kontsevich. | |
| dc.description | 42 pages, revised version, to appear in Selecta Math | |
| dc.identifier | https://arxiv.org/abs/math/0702584 | |
| dc.identifier | http://arxiv.org/abs/math/0702584 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134502 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Differential Geometry | |
| dc.title | Free Lie algebroids and the space of paths | |
| dc.type | text |