Maximal Hamiltonian tori for polygon spaces
Annales de l'Institut Fourier, Volume 53 (2003) no. 6, pp. 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: 10.5802/aif.1996
Classification: 53D20,  57S25
Keywords: polygon spaces, symplectic geometry, Hamiltonian torus actions
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.1996/

[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) (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)

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