Comptes Rendus
no. 21-22
Differential topology
The displaced disks problem via symplectic topology

Presented by: Étienne Ghys

Sobhan Seyfaddini1
1 Département de mathématiques et applications de lʼÉcole normale supérieure, 45, rue dʼUlm, 75230 Paris cedex 05, France
Comptes Rendus. Mathématique, Volume 351 (2013) no. 21-22, pp. 841-843.

We prove that a C0-small area preserving the homeomorphism of a closed surface with vanishing mass flow cannot displace a topological disk of large area. This resolves the displaced disks problem posed by F. Béguin, S. Crovisier, and F. Le Roux.

Nous démontrons quʼune petite surface C0 préservant lʼhoméomorphisme dʼune surface fermée avec un flux de masse disparaissant ne peut pas déplacer un disque topologique de grande surface. Ceci résout le problème des disques déplacés posé par F. Béguin, S. Crovisier et F. Le Roux.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.10.007

Sobhan Seyfaddini 1

1 Département de mathématiques et applications de lʼÉcole normale supérieure, 45, rue dʼUlm, 75230 Paris cedex 05, France 
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Sobhan Seyfaddini. The displaced disks problem via symplectic topology. Comptes Rendus. Mathématique, Volume 351 (2013) no. 21-22, pp. 841-843. doi : 10.1016/j.crma.2013.10.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.10.007/

[1] F. Béguin, S. Crovisier, F. Le Roux, Private communication.

[2] M. Entov; L. Polterovich; P. Py On continuity of quasimorphisms for symplectic maps, Perspectives in Analysis, Geometry, and Topology, Prog. Math., vol. 296, Birkhäuser/Springer, New York, 2012, pp. 169-197 (With an appendix by Michael Khanevsky)

[3] A. Fathi Structure of the group of homeomorphisms preserving a good measure on a compact manifold, Ann. Sci. Éc. Norm. Super. (4), Volume 13 (1980) no. 1, pp. 45-93

[4] J.-M. Gambaudo; É. Ghys Commutators and diffeomorphisms of surfaces, Ergod. Theory Dyn. Syst., Volume 24 (2004) no. 5, pp. 1591-1617

[5] P.-A. Guihéneuf Propriétés dynamiques génériques des homéomorphismes conservatifs, Ensaios Matemáticos, Mathematical Surveys, vol. 22, Sociedade Brasileira de Matemática, Rio de Janeiro, 2012

[6] A.D. Hanlon, D.N. Dore, Area preserving maps on s2: A lower bound on the c0-norm using symplectic spectral invariants, in preparation.

[7] Y.-G. Oh Construction of spectral invariants of Hamiltonian paths on closed symplectic manifolds, The Breadth of Symplectic and Poisson Geometry, Prog. Math., vol. 232, Birkhäuser Boston, Boston, MA, 2005, pp. 525-570

[8] M. Schwarz On the action spectrum for closed symplectically aspherical manifolds, Pac. J. Math., Volume 193 (2000) no. 2, pp. 419-461

[9] S. Seyfaddini C0-limits of Hamiltonian paths and the Oh–Schwarz spectral invariants, Int. Math. Res. Not. (2012) | DOI

[10] C. Viterbo Symplectic topology as the geometry of generating functions, Math. Ann., Volume 292 (1992), pp. 685-710

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