L2 -characteristic classes of Maslov–Trofimov of hamiltonian systems on the Lie algebra of the upper-triangular matrices

Jerzy Nowak

Fundamenta Mathematicae (1998)

  • Volume: 156, Issue: 2, page 99-110
  • ISSN: 0016-2736

Abstract

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We generalize the construction of Maslov-Trofimov characteristic classes to the case of some G-manifolds and use it to study certain hamiltonian systems.

How to cite

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Nowak, Jerzy. "L2 -characteristic classes of Maslov–Trofimov of hamiltonian systems on the Lie algebra of the upper-triangular matrices." Fundamenta Mathematicae 156.2 (1998): 99-110. <http://eudml.org/doc/212268>.

@article{Nowak1998,
abstract = {We generalize the construction of Maslov-Trofimov characteristic classes to the case of some G-manifolds and use it to study certain hamiltonian systems.},
author = {Nowak, Jerzy},
journal = {Fundamenta Mathematicae},
keywords = {-Maslov-Trofimov -characteristic class; symplectic manifold; Lagrangian submanifold},
language = {eng},
number = {2},
pages = {99-110},
title = {L2 -characteristic classes of Maslov–Trofimov of hamiltonian systems on the Lie algebra of the upper-triangular matrices},
url = {http://eudml.org/doc/212268},
volume = {156},
year = {1998},
}

TY - JOUR
AU - Nowak, Jerzy
TI - L2 -characteristic classes of Maslov–Trofimov of hamiltonian systems on the Lie algebra of the upper-triangular matrices
JO - Fundamenta Mathematicae
PY - 1998
VL - 156
IS - 2
SP - 99
EP - 110
AB - We generalize the construction of Maslov-Trofimov characteristic classes to the case of some G-manifolds and use it to study certain hamiltonian systems.
LA - eng
KW - -Maslov-Trofimov -characteristic class; symplectic manifold; Lagrangian submanifold
UR - http://eudml.org/doc/212268
ER -

References

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  1. [1] Arkhangel'skiĭ A.A., Completely integrable hamiltonian systems on the group of triangular matrices, Mat. Sb. 108 (1979), 134-142 (in Russian). 
  2. [2] Arnol'd V.I., On a characteristic class entering the quantization conditions, Funktsional. Anal. i Prilozhen. 1 (1) (1967), 1-14 (in Russian). 
  3. [3] Fomenko A.T., Symplectic Geometry. Methods and Applications, MGU, Moscow, 1988 (in Russian). 
  4. [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). Zbl0619.58023
  5. [5] Fomenko A.T., Morse theory of integrable hamiltonian systems, Dokl. Akad. Nauk SSSR 287 (1986), 1071-1075 (in Russian). 
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  9. [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). Zbl0521.58030
  10. [10] Fuks D.B., On Maslov-Arnold characteristic classes, Dokl. Akad. Nauk SSSR 178 (1968), 303-306 (in Russian). 
  11. [11] Guillemin V. and Sternberg S., Geometric Asymptotics, Math. Surveys 14, Amer. Math. Soc., Providence, 1977. 
  12. [12] Karasev M.V. and Vorob'ev Y.M., preprint, 1993 (in Russian). 
  13. [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). 
  14. [14] Maslov V.P., Operator Methods, Nauka, Moscow, 1973 (in Russian). 
  15. [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. 
  16. [16] Trofimov V.V., Maslov index of Lagrangian submanifolds in symplectic manifolds, Trudy Sem. Vektor. Tenzor. Anal. 23 (1988), 190-194 (in Russian). Zbl0808.53036
  17. [17] Trofimov V.V., Symplectic connections, Maslov index and Fomenko's conjecture, Dokl. Akad. Nauk SSSR 304 (1989), 214-217 (in Russian). Zbl0687.58009
  18. [18] Trofimov V.V., Connection on manifolds and new characteristic classes, Acta Appl. Math. 22 (1991), 283-312. Zbl0732.58018
  19. [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). 
  20. [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). 

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