@article{ASENS_2006_4_39_5_841_0,
author = {Zung, Nguyen Tien},
title = {Proper groupoids and momentum maps : linearization, affinity, and convexity},
journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
pages = {841--869},
year = {2006},
publisher = {Elsevier},
volume = {Ser. 4, 39},
number = {5},
doi = {10.1016/j.ansens.2006.09.002},
mrnumber = {2292634},
zbl = {1163.22001},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.ansens.2006.09.002/}
}
TY - JOUR AU - Zung, Nguyen Tien TI - Proper groupoids and momentum maps : linearization, affinity, and convexity JO - Annales scientifiques de l'École Normale Supérieure PY - 2006 SP - 841 EP - 869 VL - 39 IS - 5 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.ansens.2006.09.002/ DO - 10.1016/j.ansens.2006.09.002 LA - en ID - ASENS_2006_4_39_5_841_0 ER -
%0 Journal Article %A Zung, Nguyen Tien %T Proper groupoids and momentum maps : linearization, affinity, and convexity %J Annales scientifiques de l'École Normale Supérieure %D 2006 %P 841-869 %V 39 %N 5 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.ansens.2006.09.002/ %R 10.1016/j.ansens.2006.09.002 %G en %F ASENS_2006_4_39_5_841_0
Zung, Nguyen Tien. Proper groupoids and momentum maps : linearization, affinity, and convexity. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 39 (2006) no. 5, pp. 841-869. doi: 10.1016/j.ansens.2006.09.002
[1] , , , Lie group valued moment maps, J. Differential Geom. 48 (3) (1998) 445-495. | Zbl | MR
[2] , Compact groups of differentiable transformations, Ann. of Math. (2) 46 (1945) 372-381. | Zbl | MR
[3] , , , , Integration of twisted Dirac brackets, Duke Math. J. 123 (3) (2004) 549-607. | Zbl | MR
[4] , , , Géométrie du moment, in: Séminaire Sud-Rhodanien I, Publications du Département de Mathématiques, Univ. Claude Bernard, Lyon I, 1988, pp. 131-160. | MR
[5] , , , Groupoïdes symplectiques, in: Publications du Département de Mathématiques. Nouvelle Série A, vol. 2, Publ. Dép. Math. Nouvelle Sér. A, vol. 87, Univ. Claude Bernard, Lyon, 1987, pp. i-ii, pp. 1-62. | Zbl | MR | Numdam
[6] , , Integrability of Lie brackets, Ann. of Math. (2) 157 (2) (2003) 575-620. | Zbl | MR
[7] , , Poisson Structures and Their Normal Forms, Progr. Math., vol. 242, Birkhäuser, Basel, 2005. | Zbl | MR
[8] , Convexity and tightness for restrictions of Hamiltonian functions to fixed point sets of an antisymplectic involution, Trans. Am. Math. Soc. 275 (1983) 417-429. | Zbl | MR
[9] , , A convexity theorem for Poisson actions of compact Lie groups, Ann. Sci. École Norm. Sup. (4) 29 (6) (1996) 787-809. | Zbl | MR | Numdam
[10] , Convexity and multivalued Hamiltonians, Russ. Math. Surv. 55 (3) (2000) 578-580. | Zbl | MR
[11] , , Lie-Poisson structure on some Poisson Lie groups, J. Amer. Math. Soc. 5 (2) (1992) 445-453. | Zbl | MR
[12] , , , Group actions and curvature, Invent. Math. 23 (1974) 31-48. | Zbl | MR
[13] , , Convexity properties of the moment mapping, Invent. Math. 67 (1982) 491-513. | Zbl | MR
[14] , Groupoïdes d'holonomie et classifiants, Astérisque 116 (1984) 70-97. | Zbl | MR | Numdam
[15] , , , Symplectic convexity theorems and coadjoint orbits, Compos. Math. 94 (2) (1994) 129-180. | Zbl | MR | Numdam
[16] , Convexity properties of the moment mapping. III, Invent. Math. 77 (3) (1984) 547-552. | Zbl | MR
[17] , Convexity of Hamiltonian manifolds, J. Lie Theory 12 (2) (2002) 571-582. | Zbl | MR
[18] , Sur certains groupes de transformations de Lie, in: Géométrie différentielle. Colloques internationaux du CNRS, Strasbourg, 1953, CNRS, Paris, 1953, pp. 137-141. | Zbl | MR
[19] , Momentum mappings and reduction of Poisson actions, in: Symplectic Geometry, Groupoids, and Integrable Systems (Berkeley, CA, 1989), Math. Sci. Res. Inst. Publ., vol. 20, Springer, New York, 1991, pp. 209-226. | Zbl | MR
[20] , , Moments and reduction for symplectic groupoids, Publ. Res. Inst. Math. Sci. 24 (1) (1988) 121-140. | Zbl | MR
[21] , Sur les systèmes mécaniques dans lesquels figurent des paramètres fonctions du temps. Étude des systèmes admettant n intégrales premières uniformes en involution. Extension à ces systèmes des conditions de quantification de Bohr-Sommerfeld, Journal de l'École Polytechnique, Série III, 143ème année (1937) 173-191, 237-270. | Zbl
[22] , , Orbifolds, sheaves and groupoids, 12 (1) (1997) 3-21. | Zbl | MR
[23] , , Introduction to Foliations and Lie Groupoids, Cambridge Studies in Advanced Mathematics, vol. 91, Cambridge University Press, Cambridge, 2003, ix+173 pp. | Zbl | MR
[24] , Orbit-like foliations, in: Geometric Study of Foliations (Tokyo, 1993), World Scientific, River Edge, NJ, 1994, pp. 97-119. | MR
[25] , , Levi decomposition for smooth Poisson structures, J. Differential Geom. 68 (2) (2004) 347-395. | Zbl | MR
[26] , On the existence of slices for actions of non-compact Lie groups, Ann. of Math. (2) 73 (1961) 295-323. | Zbl | MR
[27] , Convexity properties of the moment mapping re-examined, Adv. Math. 138 (1) (1998) 46-91. | Zbl | MR
[28] , Almost invariant submanifolds for compact group actions, J. Eur. Math. Soc. (JEMS) 2 (1) (2000) 53-86. | Zbl | MR
[29] , Linearization problems for Lie algebroids and Lie groupoids, Lett. Math. Phys. 52 (1) (2000) 93-102. | Zbl | MR
[30] , Poisson geometry of discrete series orbits, and momentum convexity for noncompact group actions, Lett. Math. Phys. 56 (1) (2001) 17-30. | Zbl | MR
[31] , Linearization of regular proper groupoids, J. Inst. Math. Jussieu 1 (3) (2002) 493-511. | Zbl | MR
[32] , Momentum maps and Morita equivalence, J. Diff. Geom. 67 (2) (2004) 289-333. | Zbl | MR
[33] , Levi decomposition of analytic Poisson structures and Lie algebroids, Topology 42 (6) (2003) 1403-1420. | Zbl | MR
Cité par Sources :






