Groupoids, branched manifolds and multisections
| dc.creator | McDuff, Dusa | |
| dc.date | 2005-09-28 | |
| dc.date | 2007-06-05 | |
| dc.date.accessioned | 2026-07-07T08:07:18Z | |
| dc.date.available | 2026-07-07T08:07:18Z | |
| dc.description | Cieliebak, Mundet i Riera and Salamon recently formulated a definition of branched submanifold of Euclidean space in connection with their discussion of multivalued sections and the Euler class. This note proposes an intrinsic definition of a weighted branched manifold Z that is obtained from the usual definition of oriented orbifold groupoid by relaxing the properness condition and adding a weighting. We show that if Z is compact, finite dimensional and oriented, then it carries a fundamental class [Z]. Adapting the construction of Liu and Tian, we also show that the fundamental class [X] of any oriented orbifold X may be represented by a map from Z to X, where the branched manifold Z is unique up to a natural equivalence relation. This gives further insight into the structure of the virtual moduli cycle in the new polyfold theory recently constructed by Hofer, Wysocki and Zehnder. | |
| dc.description | 45 pages, 8 figures; v3: some definitions slightly revised, references added, v4: minor changes | |
| dc.identifier | https://arxiv.org/abs/math/0509664 | |
| dc.identifier | http://arxiv.org/abs/math/0509664 | |
| dc.identifier | Journal of Symplectic Topology, vol 4 no. 3, 259--315, 2007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130900 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Differential Geometry | |
| dc.title | Groupoids, branched manifolds and multisections | |
| dc.type | text |