Geodesic
Classification of Lagrangian fibrations
Sbornik. Mathematics, Tome 201 (2010) no. 11, pp. 1647-1688 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper classifies Lagrangian fibrations over surfaces with compact total spaces up to fibrewise symplectomorphism identical on the base. Bibliography: 15 titles.
Keywords: Lagrangian fibrations, Klein bottle. 
@article{SM_2010_201_11_a4,
     author = {I. K. Kozlov},
     title = {Classification of {Lagrangian} fibrations},
     journal = {Sbornik. Mathematics},
     pages = {1647--1688},
     year = {2010},
     volume = {201},
     number = {11},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2010_201_11_a4/}
}
TY  - JOUR
AU  - I. K. Kozlov
TI  - Classification of Lagrangian fibrations
JO  - Sbornik. Mathematics
PY  - 2010
SP  - 1647
EP  - 1688
VL  - 201
IS  - 11
UR  - http://geodesic.mathdoc.fr/item/SM_2010_201_11_a4/
LA  - en
ID  - SM_2010_201_11_a4
ER  - 
%0 Journal Article
%A I. K. Kozlov
%T Classification of Lagrangian fibrations
%J Sbornik. Mathematics
%D 2010
%P 1647-1688
%V 201
%N 11
%U http://geodesic.mathdoc.fr/item/SM_2010_201_11_a4/
%G en
%F SM_2010_201_11_a4
I. K. Kozlov. Classification of Lagrangian fibrations. Sbornik. Mathematics, Tome 201 (2010) no. 11, pp. 1647-1688. http://geodesic.mathdoc.fr/item/SM_2010_201_11_a4/

[1] A. V. Bolsinov, A. A. Oshemkov, “Singularities of integrable Hamiltonian systems”, Topological methods in the theory of integrable systems, Cambridge Sci. Publ., Cambridge, 2006, 1–67 | MR | Zbl

[2] J. J. Duistermaat, “On global action-angle coordinates”, Comm. Pure Appl. Math., 33:6 (1980), 687–706 | DOI | MR | Zbl

[3] N. T. Zung, “Symplectic topology of integrable Hamiltonian systems. II: Topological classification”, Compositio Math., 138:2 (2003), 125–156 | DOI | MR | Zbl

[4] K. N. Mishachev, “The classification of Lagrangian bundles over surfaces”, Differential Geom. Appl., 6:4 (1996), 301–320 | DOI | MR | Zbl

[5] S.-T. Hu, Homotopy theory, Academic Press, New York–London, 1959 | MR | Zbl | Zbl

[6] A. T. Fomenko, D. B. Fuks, Kurs gomotopicheskoi topologii, Nauka, M., 1989 | MR | Zbl

[7] B. A. Dubrovin, A. T. Fomenko, S. P. Novikov, Modern geometry – methods and applications. Part I. The geometry of surfaces, transformation groups, and fields, Grad. Texts in Math., 93, Springer-Verlag, New York, 1992 | MR | MR | Zbl | Zbl

[8] J. Milnor, “On the existence of a connection with curvature zero”, Comment. Math. Helv., 32 (1958), 215–223 | DOI | MR | Zbl

[9] D. Freid, W. Goldman, M. W. Hirsh, “Affine manifolds with nilpotent holonomy”, Comment. Math. Helv., 56:4 (1981), 487–523 | DOI | MR

[10] W. Magnus, A. Karrass, D. Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Interscience Publ., New York–London–Sydney, 1966 | MR | MR | Zbl | Zbl

[11] N. T. Zung, “Symplectic topology of integrable Hamiltonian systems. I: Arnold–Liouville with singularities”, Compositio Math., 101:2 (1996), 179–215 | MR | Zbl

[12] M. Symington, “Four dimensions from two in symplectic topology”, Topology and geometry of manifolds (University of Georgia, Athens, GA, USA, 2001), Proc. Sympos. Pure Math., 71, Amer. Math. Soc., Providence, RI, 2003, 153–208 | MR | Zbl

[13] N. C. Leung, M. Symington, “Almost toric symplectic four-manifolds”, J. Symplectic Geom., 8:2 (2010), 143–187 | MR | Zbl

[14] S. P. Novikov, “The Hamiltonian formalism and a many-valued analogue of Morse theory”, Russian Math. Surveys, 37:5 (1982), 1–56 | DOI | MR | Zbl

[15] D. Sepe, Classification of Lagrangian fibrations over a Klein bottle, arXiv: 0909.2982