Volume 10, issue 2 (2010)

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Convexity package for momentum maps on contact manifolds

River Chiang and Yael Karshon

Algebraic & Geometric Topology 10 (2010) 925–977
Bibliography
1 C Albert, Le théorème de réduction de Marsden–Weinstein en géométrie cosymplectique et de contact, J. Geom. Phys. 6 (1989) 627 MR1076705
2 M F Atiyah, Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14 (1982) 1 MR642416
3 A Banyaga, P Molino, Géométrie des formes de contact complètement intégrables de type toriques, from: "Séminaire Gaston Darboux de Géométrie et Topologie Différentielle, 1991–1992 (Montpellier)", Univ. Montpellier II (1993) 1 MR1223155
4 A Barvinok, A course in convexity, Graduate Studies in Math. 54, Amer. Math. Soc. (2002) MR1940576
5 M Berger, Geometry. I, Universitext, Springer (1987) MR882541
6 M Berger, Geometry. II, Universitext, Springer (1987) MR882916
7 P Birtea, J P Ortega, T S Ratiu, A local-to-global principle for convexity in metric spaces, J. Lie Theory 18 (2008) 445 MR2431127
8 P Birtea, J P Ortega, T S Ratiu, Openness and convexity for momentum maps, Trans. Amer. Math. Soc. 361 (2009) 603 MR2452817
9 C Bjorndahl, Y Karshon, Revisiting Tietze–Nakajima – local and global convexity for maps, to appear in the Canad. J. Math. arXiv:math/0701745v4
10 C P Boyer, K Galicki, A note on toric contact geometry, J. Geom. Phys. 35 (2000) 288 MR1780757
11 M R Bridson, A Haefliger, Metric spaces of non-positive curvature, Grund. der Math. Wissenschaften 319, Springer (1999) MR1744486
12 M Condevaux, P Dazord, P Molino, Géométrie du moment, from: "Travaux du Séminaire Sud-Rhodanien de Géométrie, I", Publ. Dép. Math. Nouvelle Sér. B 88, Univ. Claude-Bernard (1988) 131 MR1040871
13 L Danzer, B Grünbaum, V Klee, Helly's theorem and its relatives, from: "Proc. Sympos. Pure Math., Vol. VII", Amer. Math. Soc. (1963) 101 MR0157289
14 H Geiges, Constructions of contact manifolds, Math. Proc. Cambridge Philos. Soc. 121 (1997) 455 MR1434654
15 H Geiges, An introduction to contact topology, Cambridge Studies in Advanced Math. 109, Cambridge Univ. Press (2008) MR2397738
16 V Guillemin, R Sjamaar, Convexity properties of Hamiltonian group actions, CRM Monogr. Ser. 26, Amer. Math. Soc. (2005) MR2175783
17 V Guillemin, S Sternberg, Convexity properties of the moment mapping, Invent. Math. 67 (1982) 491 MR664117
18 V Guillemin, S Sternberg, Homogeneous quantization and multiplicities of group representations, J. Funct. Anal. 47 (1982) 344 MR665022
19 J Hilgert, K H Neeb, W Plank, Symplectic convexity theorems, Sem. Sophus Lie 3 (1993) 123 MR1270171
20 J Hilgert, K H Neeb, W Plank, Symplectic convexity theorems and coadjoint orbits, Compositio Math. 94 (1994) 129 MR1302314
21 Y Kamishima, T Tsuboi, CR-structures on Seifert manifolds, Invent. Math. 104 (1991) 149 MR1094049
22 F Knop, Convexity of Hamiltonian manifolds, J. Lie Theory 12 (2002) 571 MR1923787
23 E Lerman, Contact cuts, Israel J. Math. 124 (2001) 77 MR1856505
24 E Lerman, A convexity theorem for torus actions on contact manifolds, Illinois J. Math. 46 (2002) 171 MR1936083
25 E Lerman, Contact toric manifolds, J. Symplectic Geom. 1 (2003) 785 MR2039164
26 E Lerman, E Meinrenken, S Tolman, C Woodward, Nonabelian convexity by symplectic cuts, Topology 37 (1998) 245 MR1489203
27 E Lerman, C Willett, The topological structure of contact and symplectic quotients, Internat. Math. Res. Notices (2001) 33 MR1809496
28 F Loose, Reduction in contact geometry, J. Lie Theory 11 (2001) 9 MR1828281
29 S F B de Moraes, C Tomei, Moment maps on symplectic cones, Pacific J. Math. 181 (1997) 357 MR1486536
30 S Nakajima, Über konvexe Kurven und Flächen, Tohoku Math. J. 29 (1928) 227
31 H Nozawa, Five dimensional $K$–contact manifolds of rank 2 arXiv:0907.0208v1
32 E Prato, Convexity properties of the moment map for certain non-compact manifolds, Comm. Anal. Geom. 2 (1994) 267 MR1312689
33 C V Robinson, Spherical theorems of Helly type and congruence indices of spherical caps, Amer. J. Math. 64 (1942) 260 MR0006420
34 R Sjamaar, Convexity properties of the moment mapping re-examined, Adv. Math. 138 (1998) 46 MR1645052
35 H Tietze, Über Konvexheit im kleinen und im gro\ss en und über gewisse den Punkten einer Menge zugeordnete Dimensionszahlen, Math. Z. 28 (1928) 697 MR1544985
36 C Willett, Contact reduction, Trans. Amer. Math. Soc. 354 (2002) 4245 MR1926873