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- W86888384 abstract "Let M and N be closed n-dimensional manifolds, and equip N with a volume form sigma. Let mu be an exact n-form on M. Arnold then asked the question: When can one find a map f:;N such that f*sigma=mu. 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 mu one 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 mu from sigma, 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." @default.
- W86888384 created "2016-06-24" @default.
- W86888384 creator A5051225949 @default.
- W86888384 date "2005-12-06" @default.
- W86888384 modified "2023-09-27" @default.
- W86888384 title "Failure of the parametric h-principle for maps with prescribed jacobian" @default.
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