Inner and outer hamiltonian capacities

David Hermann

Bulletin de la Société Mathématique de France (2004)

  • Volume: 132, Issue: 4, page 509-541
  • ISSN: 0037-9484

Abstract

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The aim of this paper is to compare two symplectic capacities in ℂ n related with periodic orbits of Hamiltonian systems: the Floer-Hofer capacity arising from symplectic homology, and the Viterbo capacity based on generating functions. It is shown here that the inner Floer-Hofer capacity is not larger than the Viterbo capacity and that they are equal for open sets with restricted contact type boundary. As an application, we prove that the Viterbo capacity of any compact Lagrangian submanifold is nonzero.

How to cite

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Hermann, David. "Inner and outer hamiltonian capacities." Bulletin de la Société Mathématique de France 132.4 (2004): 509-541. <http://eudml.org/doc/272349>.

@article{Hermann2004,
abstract = {The aim of this paper is to compare two symplectic capacities in $\mathbb \{C\}^n$ related with periodic orbits of Hamiltonian systems: the Floer-Hofer capacity arising from symplectic homology, and the Viterbo capacity based on generating functions. It is shown here that the inner Floer-Hofer capacity is not larger than the Viterbo capacity and that they are equal for open sets with restricted contact type boundary. As an application, we prove that the Viterbo capacity of any compact Lagrangian submanifold is nonzero.},
author = {Hermann, David},
journal = {Bulletin de la Société Mathématique de France},
keywords = {symplectic capacities; lagrangian submanifolds},
language = {eng},
number = {4},
pages = {509-541},
publisher = {Société mathématique de France},
title = {Inner and outer hamiltonian capacities},
url = {http://eudml.org/doc/272349},
volume = {132},
year = {2004},
}

TY - JOUR
AU - Hermann, David
TI - Inner and outer hamiltonian capacities
JO - Bulletin de la Société Mathématique de France
PY - 2004
PB - Société mathématique de France
VL - 132
IS - 4
SP - 509
EP - 541
AB - The aim of this paper is to compare two symplectic capacities in $\mathbb {C}^n$ related with periodic orbits of Hamiltonian systems: the Floer-Hofer capacity arising from symplectic homology, and the Viterbo capacity based on generating functions. It is shown here that the inner Floer-Hofer capacity is not larger than the Viterbo capacity and that they are equal for open sets with restricted contact type boundary. As an application, we prove that the Viterbo capacity of any compact Lagrangian submanifold is nonzero.
LA - eng
KW - symplectic capacities; lagrangian submanifolds
UR - http://eudml.org/doc/272349
ER -

References

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  11. [11] —, « A complete proof of Viterbo’s uniqueness theorem on generating functions », Topology Appl. 96 (1999), no. 3, p. 246–266. Zbl0952.53037MR1709692
  12. [12] L. Traynor – « Symplectic homology via generating functions », Geom. Funct. Anal. 4 (1994), no. 6, p. 718–748. Zbl0822.58020MR1302337
  13. [13] C. Viterbo – « A new obstruction to embedding Lagrangian tori », Invent. Math.100 (1990), p. 301–320. Zbl0727.58015MR1047136
  14. [14] —, « Symplectic topology as the geometry of generating functions », Math. Ann.292 (1992), p. 685–710. Zbl0735.58019MR1157321
  15. [15] —, « Functors and computations in Floer homology with applications II », (1998), Preprint Université Paris-Sud 98-15. To appear in GAFA. 
  16. [16] —, « Functors and computations in Floer homology with applications I », Geom. Funct. Anal. 9 (1999), no. 5, p. 985–1033. Zbl0954.57015MR1726235

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