The Liouville phenomenon in the deformation problem of coisotropics
| dc.creator | Kieserman, Noah | |
| dc.date | 2008-05-16 | |
| dc.date.accessioned | 2026-07-07T09:41:03Z | |
| dc.date.available | 2026-07-07T09:41:03Z | |
| dc.description | The work of Oh and Park ([OP]) on the deformation problem of coisotropic submanifolds opened the possibility of studying a large and interesting class of foliations with some explicit geometric tools. These tools assemble into the structure of an L-infinity algebra on the shifted foliation complex (Ω^*[1](\fol), d_\fol), which allows a concise description of deformations in terms of a Maurer-Cartan equation. Infinitesimal deformations are given by d_\fol-closed forms, and the relation between infinitesimal deformations and full deformations can be studied in terms of obstruction classes lying in the foliation cohomology H^*_\fol. Closely related to the foliation cohomology is Haefliger's group Ω^*_c(T/H), an under-appreciated model for the leaf space of a foliation. We make integral use of this group in showing solvability and unsolvability of the obstruction equations. We also show the L-infinity apparatus to be capable of detecting the Liouville/diophantine distinction of KAM theory, and argue for the greater significance of Haefliger's integration-over-leaves map in passing this fine structure to a geometric model for the leaf space. | |
| dc.description | 27 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/0805.2468 | |
| dc.identifier | http://arxiv.org/abs/0805.2468 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161691 | |
| dc.subject | Geometric Topology | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 57R30; 70G45; 32G10 | |
| dc.title | The Liouville phenomenon in the deformation problem of coisotropics | |
| dc.type | text |