Maximal Hamiltonian tori for polygon spaces
Annales de l'Institut Fourier, Volume 53 (2003) no. 6, p. 1925-1939

We study the poset of Hamiltonian tori for polygon spaces. We determine some maximal elements and give examples where maximal Hamiltonian tori are not all of the same dimension.

On étudie l'ensemble partiellement ordonné des tores hamiltoniens pour les espaces de polygones. Un certain nombre d'éléments maximaux sont dégagés et l'on donne des exemples où les tores maximaux n'ont pas tous la même dimension.

DOI : https://doi.org/10.5802/aif.1996
Classification:  53D20,  57S25
Keywords: polygon spaces, symplectic geometry, Hamiltonian torus actions
@article{AIF_2003__53_6_1925_0,
     author = {Hausmann, Jean-Claude and Tolman, Susan},
     title = {Maximal Hamiltonian tori for polygon spaces},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {53},
     number = {6},
     year = {2003},
     pages = {1925-1939},
     doi = {10.5802/aif.1996},
     zbl = {1049.53056},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2003__53_6_1925_0}
}
Hausmann, Jean-Claude; Tolman, Susan. Maximal Hamiltonian tori for polygon spaces. Annales de l'Institut Fourier, Volume 53 (2003) no. 6, pp. 1925-1939. doi : 10.5802/aif.1996. http://www.numdam.org/item/AIF_2003__53_6_1925_0/

[Au] M. Audin The topology of torus actions on symplectic manifolds, Birkhäuser (1991) | MR 1106194 | Zbl 0726.57029

[BW] W.M. Boothby; H.C. Wang On contact manifolds, Ann. of Math. (2), Tome 68 (1958), pp. 721-734 | Article | MR 112160 | Zbl 0084.39204

[De] T. Delzant Hamiltoniens périodiques et image convexe de l'application moment, Bull. Soc. Math. France, Tome 116 (1988), pp. 315-339 | Numdam | MR 984900 | Zbl 0676.58029

[Ha] J-C. Hausmann Sur la topologie des bras articulés, Algebraic Topology, Poznan (Springer Lectures Notes) Tome 1474 (1989), pp. 146-159 | Zbl 0736.57014

[HK1] J-C. Hausmann; A. Knutson The cohomology ring of polygon spaces. Grasmannians, Annales de l'Institut Fourier, Tome 48 (1998) no. 1, pp. 281-321 | Article | Numdam | MR 1614965 | Zbl 0903.14019

[HK2] J-C. Hausmann; A. Knutson A limit of toric symplectic forms that has no periodic Hamiltonians, GAFA, Geom. Funct. Anal, Tome 10 (2000), pp. 556-562 | Article | MR 1779612 | Zbl 0984.53031

[Ka] Y. Karshon Maximal tori in the symplectomorphism groups of Hirzebruch surfaces, Math. Res. Lett, Tome 10 (2003) no. 1, pp. 125-132 | MR 1960129 | Zbl 1036.53063

[Kl] A. Klyachko Spatial polygons and stable configurations of points in the projective line, Algebraic geometry and its applications (Yaroslav/\cprime, 1992), Vieweg, Braunschweig (Aspects Math.) (1992), pp. 67-84 | Zbl 0820.51016

[KM] M. Kapovich; J. Millson The symplectic geometry of polygons in Euclidean space, J. of Diff. Geometry, Tome 44 (1996), pp. 479-513 | MR 1431002 | Zbl 0889.58017

[Le] E. Lerman On maximal tori in the contactomorphism groups of regular contact manifolds (2002) (e-print, math.SG/0212043)