Maximal Hamiltonian tori for polygon spaces

Jean-Claude Hausmann[1]; Susan Tolman[2]

  • [1] Université de Genève, Section de Mathématiques, B.P. 240, CH-1211 Genève 24
  • [2] University of Illinois at Urbana-Champaign, Department of Mathematics, Urbana, IL 61801 (USA)

Annales de l’institut Fourier (2003)

  • Volume: 53, Issue: 6, page 1925-1939
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Hausmann, Jean-Claude, and Tolman, Susan. "Maximal Hamiltonian tori for polygon spaces." Annales de l’institut Fourier 53.6 (2003): 1925-1939. <http://eudml.org/doc/116089>.

@article{Hausmann2003,
abstract = {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.},
affiliation = {Université de Genève, Section de Mathématiques, B.P. 240, CH-1211 Genève 24; University of Illinois at Urbana-Champaign, Department of Mathematics, Urbana, IL 61801 (USA)},
author = {Hausmann, Jean-Claude, Tolman, Susan},
journal = {Annales de l’institut Fourier},
keywords = {polygon spaces; symplectic geometry; Hamiltonian torus actions},
language = {eng},
number = {6},
pages = {1925-1939},
publisher = {Association des Annales de l'Institut Fourier},
title = {Maximal Hamiltonian tori for polygon spaces},
url = {http://eudml.org/doc/116089},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Hausmann, Jean-Claude
AU - Tolman, Susan
TI - Maximal Hamiltonian tori for polygon spaces
JO - Annales de l’institut Fourier
PY - 2003
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 6
SP - 1925
EP - 1939
AB - 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.
LA - eng
KW - polygon spaces; symplectic geometry; Hamiltonian torus actions
UR - http://eudml.org/doc/116089
ER -

References

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  1. M. Audin, The topology of torus actions on symplectic manifolds, (1991), Birkhäuser Zbl0726.57029MR1106194
  2. W.M. Boothby, H.C. Wang, On contact manifolds, Ann. of Math. (2) 68 (1958), 721-734 Zbl0084.39204MR112160
  3. T. Delzant, Hamiltoniens périodiques et image convexe de l'application moment, Bull. Soc. Math. France 116 (1988), 315-339 Zbl0676.58029MR984900
  4. J-C. Hausmann, A. Knutson, The cohomology ring of polygon spaces. Grasmannians, Annales de l'Institut Fourier 48 (1998), 281-321 Zbl0903.14019MR1614965
  5. J-C. Hausmann, A. Knutson, A limit of toric symplectic forms that has no periodic Hamiltonians, GAFA, Geom. Funct. Anal 10 (2000), 556-562 Zbl0984.53031MR1779612
  6. J-C. Hausmann, Sur la topologie des bras articulés, Algebraic Topology, Poznan 1474 (1989), 146-159 Zbl0736.57014
  7. M. Kapovich, J. Millson, The symplectic geometry of polygons in Euclidean space, J. of Diff. Geometry 44 (1996), 479-513 Zbl0889.58017MR1431002
  8. Y. Karshon, Maximal tori in the symplectomorphism groups of Hirzebruch surfaces, Math. Res. Lett 10 (2003), 125-132 Zbl1036.53063MR1960129
  9. A. Klyachko, Spatial polygons and stable configurations of points in the projective line, Algebraic geometry and its applications (Yaroslav/, 1992) (1992), 67-84, Vieweg, Braunschweig Zbl0820.51016
  10. E. Lerman, On maximal tori in the contactomorphism groups of regular contact manifolds, (2002) 

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