Geodesic
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
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {1997},
     volume = {188},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_1_a3/}
}
TY  - JOUR
AU  - B. S. Kruglikov
TI  - The image in $H^2(Q^3;\mathbb R)$ of the set of presymplectic forms with a prescribed kernel
JO  - Sbornik. Mathematics
PY  - 1997
SP  - 75
EP  - 85
VL  - 188
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1997_188_1_a3/
LA  - en
ID  - SM_1997_188_1_a3
ER  - 
%0 Journal Article
%A B. S. Kruglikov
%T The image in $H^2(Q^3;\mathbb R)$ of the set of presymplectic forms with a prescribed kernel
%J Sbornik. Mathematics
%D 1997
%P 75-85
%V 188
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1997_188_1_a3/
%G en
%F 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/

[1] Hofer H., Zehnder E., Symplectic Invariants and Hamiltonian Dynamics, Birkhäuser, 1994 | MR

[2] Weinstein A., Lectures on symplectic manifolds (North Carolina), Regional Conf. Ser. in Math., 29, Amer. Math. Soc., Providence, RI, 1977 | MR | Zbl

[3] Arnold V. I., Givental A. B., “Simplekticheskaya geometriya”, Dinamicheskie sistemy–4, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 4, 1985, 5–139 | MR

[4] Kruglikov B. S., “O prodolzhenii simplekticheskoi struktury”, Trudy seminara po tenzornomu i vektornomu analizu, 25:1 (1993), 71–75 | MR

[5] Fomenko A. T., Simplekticheskaya geometriya. Metody i prilozheniya, Izd-vo MGU, M., 1988 | MR | Zbl

[6] Bolsinov A. V., Matveev S. V., Fomenko A. T., “Topologicheskaya klassifikatsiya integriruemykh gamiltonovykh sistem s dvumya stepenyami svobody. Spisok sistem maloi slozhnosti”, UMN, 45:2 (1990), 59–77 | MR | Zbl

[7] Kruglikov B. S., “Suschestvovanie pary dopolnitelnykh bottovskikh integralov dlya rezonansnoi gamiltonovoi sistemy s dvumya stepenyami svobody”, Trudy MIRAN, 205, Nauka, M., 1994, 109–112 | MR | Zbl

[8] Bolsinov A. V., Fomenko A. T., “Traektornaya ekvivalentnost integriruemykh gamiltonovykh sistem s dvumya stepenyami svobody. Teorema klassifikatsii. I; II”, Matem. sb., 185:4 (1994), 27–80 ; 5, 27–78 | MR | Zbl

[9] Nguen Tien Zung, Symplectic topology of integrable Hamiltonian systems, Preprint of ICTP, IC/93/305, Trieste, 1993

[10] Fomenko A. T., “Topologicheskii invariant, grubo klassifitsiruyuschii integriruemye strogo nevyrozhdennye gamiltoniany na chetyrekhmernykh simplekticheskikh mnogoobraziyakh”, Funktsion. analiz i ego prilozh., 25:4 (1991), 23–35 | MR

[11] Bolsinov A. V., “Gladkaya traektornaya ekvivalentnost integriruemykh gamiltonovykh sistem s dvumya stepenyami svobody”, Matem. sb., 186:1 (1995), 3–28 | MR | Zbl

[12] Kruglikov B. S., Tochnaya gladkaya klassifikatsiya gamiltonovykh sistem na dvumernykh mnogoobraziyakh, Preprint of ICTP, Nov. 1994, IC/94/314, Trieste

[13] Topalov P., “Peremennaya deistviya i gamiltonian Puankare v okrestnosti kriticheskoi okruzhnosti”, UMN, 50:1 (1995), 213–214 | MR | Zbl

[14] Orlik P., Seifert manifolds, Lecture Notes in Math., 291, 1972 | MR | Zbl

[15] Raymond F., “Classification of the actions of the circle on $3$-manifolds”, Trans. Amer. Math. Soc., 131 (1968), 51–78 | DOI | MR | Zbl

[16] Seifert H., “Topologie driedimensionaler gefaserte Räume”, Acta Math., 60 (1933), 147–238 | DOI | MR | Zbl