@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}, publisher = {Elsevier}, volume = {Ser. 4, 39}, number = {5}, year = {2006}, doi = {10.1016/j.ansens.2006.09.002}, mrnumber = {2292634}, zbl = {1163.22001}, language = {en}, url = {http://archive.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 - http://archive.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 http://archive.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. http://archive.numdam.org/articles/10.1016/j.ansens.2006.09.002/
[1] Lie group valued moment maps, J. Differential Geom. 48 (3) (1998) 445-495. | MR | Zbl
, , ,[2] Compact groups of differentiable transformations, Ann. of Math. (2) 46 (1945) 372-381. | MR | Zbl
,[3] Integration of twisted Dirac brackets, Duke Math. J. 123 (3) (2004) 549-607. | MR | Zbl
, , , ,[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. | Numdam | MR | Zbl
, , ,[6] Integrability of Lie brackets, Ann. of Math. (2) 157 (2) (2003) 575-620. | MR | Zbl
, ,[7] Poisson Structures and Their Normal Forms, Progr. Math., vol. 242, Birkhäuser, Basel, 2005. | MR | Zbl
, ,[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. | MR | Zbl
,[9] A convexity theorem for Poisson actions of compact Lie groups, Ann. Sci. École Norm. Sup. (4) 29 (6) (1996) 787-809. | Numdam | MR | Zbl
, ,[10] Convexity and multivalued Hamiltonians, Russ. Math. Surv. 55 (3) (2000) 578-580. | MR | Zbl
,[11] Lie-Poisson structure on some Poisson Lie groups, J. Amer. Math. Soc. 5 (2) (1992) 445-453. | MR | Zbl
, ,[12] Group actions and curvature, Invent. Math. 23 (1974) 31-48. | MR | Zbl
, , ,[13] Convexity properties of the moment mapping, Invent. Math. 67 (1982) 491-513. | MR | Zbl
, ,[14] Groupoïdes d'holonomie et classifiants, Astérisque 116 (1984) 70-97. | Numdam | MR | Zbl
,[15] Symplectic convexity theorems and coadjoint orbits, Compos. Math. 94 (2) (1994) 129-180. | Numdam | MR | Zbl
, , ,[16] Convexity properties of the moment mapping. III, Invent. Math. 77 (3) (1984) 547-552. | MR | Zbl
,[17] Convexity of Hamiltonian manifolds, J. Lie Theory 12 (2) (2002) 571-582. | MR | Zbl
,[18] Sur certains groupes de transformations de Lie, in: Géométrie différentielle. Colloques internationaux du CNRS, Strasbourg, 1953, CNRS, Paris, 1953, pp. 137-141. | MR | Zbl
,[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. | MR | Zbl
,[20] Moments and reduction for symplectic groupoids, Publ. Res. Inst. Math. Sci. 24 (1) (1988) 121-140. | MR | Zbl
, ,[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. | MR | Zbl
, ,[23] Introduction to Foliations and Lie Groupoids, Cambridge Studies in Advanced Mathematics, vol. 91, Cambridge University Press, Cambridge, 2003, ix+173 pp. | MR | Zbl
, ,[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. | MR | Zbl
, ,[26] On the existence of slices for actions of non-compact Lie groups, Ann. of Math. (2) 73 (1961) 295-323. | MR | Zbl
,[27] Convexity properties of the moment mapping re-examined, Adv. Math. 138 (1) (1998) 46-91. | MR | Zbl
,[28] Almost invariant submanifolds for compact group actions, J. Eur. Math. Soc. (JEMS) 2 (1) (2000) 53-86. | MR | Zbl
,[29] Linearization problems for Lie algebroids and Lie groupoids, Lett. Math. Phys. 52 (1) (2000) 93-102. | MR | Zbl
,[30] Poisson geometry of discrete series orbits, and momentum convexity for noncompact group actions, Lett. Math. Phys. 56 (1) (2001) 17-30. | MR | Zbl
,[31] Linearization of regular proper groupoids, J. Inst. Math. Jussieu 1 (3) (2002) 493-511. | MR | Zbl
,[32] Momentum maps and Morita equivalence, J. Diff. Geom. 67 (2) (2004) 289-333. | MR | Zbl
,[33] Levi decomposition of analytic Poisson structures and Lie algebroids, Topology 42 (6) (2003) 1403-1420. | MR | Zbl
,Cité par Sources :