Failure of the parametric h-principle for maps with prescribed jacobian
| dc.creator | Coffey, Joseph | |
| dc.date | 2005-12-06 | |
| dc.date.accessioned | 2026-07-07T06:54:55Z | |
| dc.date.available | 2026-07-07T06:54:55Z | |
| dc.description | Let M and N be closed n-dimensional manifolds, and equip N with a volume form σ. Let μbe an exact n-form on M. Arnold then asked the question: When can one find a map f:;N such that f*σ=μ. In 1973 Eliashberg and Gromov showed that this problem is, in a deep sense, trivial: It satisfies an h-principle, and whenever one can find a bundle map f_bdl:T M to T N which is degree 0 on the base and induces μone can homotop this map to a solution f. That is if the naive topological conditions are satisfied on can find a solution. There is no further interesting geometry in the problem. We show the corresponding parametric h-principle fails- if one considers families of maps inducing μfrom σ, one can find interesting topology in the space of solutions which is not predicted by an h-principle. Moreover the homotopy type of such maps is quantized: for certain families of forms homotopy type remains constant, jumping only at discrete values. | |
| dc.description | 26 pages. 6 figures | |
| dc.identifier | https://arxiv.org/abs/math/0512126 | |
| dc.identifier | http://arxiv.org/abs/math/0512126 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106110 | |
| dc.subject | Geometric Topology | |
| dc.subject | Algebraic Topology | |
| dc.subject | Differential Geometry | |
| dc.subject | 57R45 | |
| dc.title | Failure of the parametric h-principle for maps with prescribed jacobian | |
| dc.type | text |