The image in $H^2(Q^3;\mathbb R)$ of the~set of presymplectic forms with a~prescribed kernel
Sbornik. Mathematics, Tome 188 (1997) no. 1, pp. 75-85
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A new invariant $\Omega$ of a 1-distribution $\mathscr I$ on a closed 3-dimensional manifold $Q^3$ is defined as the domain in the second cohomology group $H^2(Q^3;\mathbb R)$ generated by the restrictions to $Q^3=Q^3\times \{0\}$ of all symplectic forms $\omega$ on $Q^3\times \mathbb R$ such that the kernel of the restriction $\omega \big |_{Q^3}$ is the 1-distribution $\mathscr I$ (that is, $\mathscr I$ is the characteristic distribution of this restriction). This invariant is calculated in the cases when the distribution $\mathscr I$ is non-integrable, Bott non-resonance integrable, and resonance integrable.
@article{SM_1997_188_1_a3,
author = {B. S. Kruglikov},
title = {The image in $H^2(Q^3;\mathbb R)$ of the~set of presymplectic forms with a~prescribed kernel},
journal = {Sbornik. Mathematics},
pages = {75--85},
publisher = {mathdoc},
volume = {188},
number = {1},
year = {1997},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1997_188_1_a3/}
}
B. S. Kruglikov. The image in $H^2(Q^3;\mathbb R)$ of the~set of presymplectic forms with a~prescribed kernel. Sbornik. Mathematics, Tome 188 (1997) no. 1, pp. 75-85. http://geodesic.mathdoc.fr/item/SM_1997_188_1_a3/