We generalize the construction of Maslov-Trofimov characteristic classes to the case of some G-manifolds and use it to study certain hamiltonian systems.
@article{bwmeta1.element.bwnjournal-article-fmv156i2p99bwm,
author = {Jerzy Nowak},
title = {L2 -characteristic classes of Maslov--Trofimov of hamiltonian systems on the Lie algebra of the upper-triangular matrices},
journal = {Fundamenta Mathematicae},
volume = {158},
year = {1998},
pages = {99-110},
zbl = {0911.53017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv156i2p99bwm}
}
Nowak, Jerzy. L2 -characteristic classes of Maslov–Trofimov of hamiltonian systems on the Lie algebra of the upper-triangular matrices. Fundamenta Mathematicae, Tome 158 (1998) pp. 99-110. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv156i2p99bwm/
[00000] [1] Arkhangel'skiĭ A.A., Completely integrable hamiltonian systems on the group of triangular matrices, Mat. Sb. 108 (1979), 134-142 (in Russian).
[00001] [2] Arnol'd V.I., On a characteristic class entering the quantization conditions, Funktsional. Anal. i Prilozhen. 1 (1) (1967), 1-14 (in Russian).
[00002] [3] Fomenko A.T., Symplectic Geometry. Methods and Applications, MGU, Moscow, 1988 (in Russian).
[00003] [4] Fomenko A.T., Topology of isoenergy surfaces of integrable hamiltonian systems and obstructions to integrability, Izv. Akad. Nauk SSSR Ser. Mat. 50 (1986), 1276-1307 (in Russian). | Zbl 0619.58023
[00004] [5] Fomenko A.T., Morse theory of integrable hamiltonian systems, Dokl. Akad. Nauk SSSR 287 (1986), 1071-1075 (in Russian).
[00005] [6] Fomenko A.T., Topological invariants of hamiltonian systems, integrable in the sense of Liouville, Funktsional. Anal. i Prilozhen. 22 (4) (1988), 38-51 (in Russian).
[00006] [7] Fomenko A.T., On symplectic structures and integrable systems on symmetric spaces, Mat. Sb. 115 (1981), 38-51 (in Russian).
[00007] [8] Fomenko A.T. and Le Hong Van, A criterion of minimality of Lagrangian submanifolds in Kählerian manifolds, Mat. Zametki 4 (1987), 559-571 (in Russian). | Zbl 0633.53082
[00008] [9] Fomenko A.T. and Trofimov V.V., Group non-invariant symplectic structures and hamiltonian flows on symmetric spaces, Trudy Sem. Vektor. Tenzor. Anal. 21 (1983), 23-83 (in Russian). | Zbl 0521.58030
[00009] [10] Fuks D.B., On Maslov-Arnold characteristic classes, Dokl. Akad. Nauk SSSR 178 (1968), 303-306 (in Russian).
[00010] [11] Guillemin V. and Sternberg S., Geometric Asymptotics, Math. Surveys 14, Amer. Math. Soc., Providence, 1977.
[00011] [12] Karasev M.V. and Vorob'ev Y.M., preprint, 1993 (in Russian).
[00012] [13] Le Hong Van, Minimal surfaces and Maslov-Trofimov index, in: Izbrannye Voprosy Algebry, Geom. i Diskr. Matem., MGU, Moscow, 1988, 62-79 (in Russian).
[00013] [14] Maslov V.P., Operator Methods, Nauka, Moscow, 1973 (in Russian).
[00014] [15] McDuff D., Elliptic methods in symplectic geometry, lecture notes distributed in conjunction with the Progress in Mathematics Lecture given at the 92nd summer meeting of the American Mathematical Society, University of Colorado, Boulder, 1989.
[00015] [16] Trofimov V.V., Maslov index of Lagrangian submanifolds in symplectic manifolds, Trudy Sem. Vektor. Tenzor. Anal. 23 (1988), 190-194 (in Russian). | Zbl 0808.53036
[00016] [17] Trofimov V.V., Symplectic connections, Maslov index and Fomenko's conjecture, Dokl. Akad. Nauk SSSR 304 (1989), 214-217 (in Russian). | Zbl 0687.58009
[00017] [18] Trofimov V.V., Connection on manifolds and new characteristic classes, Acta Appl. Math. 22 (1991), 283-312. | Zbl 0732.58018
[00018] [19] Trofimov V.V., Holonomy group and generalized Maslov classes on submanifolds in spaces with an affine connection, Mat. Zametki 49 (1991), 113-123 (in Russian).
[00019] [20] Trofimov V.V., Euler equations on Borel subalgebras of semisimple Lie algebras, Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979), 714-732 (in Russian).