Geodesic
Differential Geometry
On the bounded isometry conjecture
[Sur la conjecture dʼisométrie bornée]

Présenté par : the Editorial Board

Pedroza, Andrés1
1 Facultad de Ciencias, Universidad de Colima, Bernal Díaz del Castillo No. 340, Colima, Col., Mexico 28045
Comptes Rendus. Mathématique, Tome 349 (2011) no. 19-20, pp. 1097-1100.

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We prove the bounded isometry conjecture proposed by F. Lalonde and L. Polterovich for a special class of closed symplectic manifolds.

Nous prouvons la conjecture dʼisométrie bornée proposée par F. Lalonde et L. Polterovich pour une classe spéciale de variétés symplectiques fermées.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2011.08.016

Pedroza, Andrés 1

1 Facultad de Ciencias, Universidad de Colima, Bernal Díaz del Castillo No. 340, Colima, Col., Mexico 28045 
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Pedroza, Andrés. On the bounded isometry conjecture. Comptes Rendus. Mathématique, Tome 349 (2011) no. 19-20, pp. 1097-1100. doi : 10.1016/j.crma.2011.08.016. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2011.08.016/

[1] C. Campos-Apanco, A. Pedroza, Bounded symplectic diffeomorphisms and split flux groups, Proc. of Amer. Math. Soc., in press.

[2] Han, Z. Bi-invariant metrics on the group of symplectomorphisms, Trans. Amer. Math. Soc., Volume 361 (2009), pp. 3343-3357

[3] Han, Z. The bounded isometry conjecture for the Kodaira–Thurston manifold and 4-torus, Israel J. Math., Volume 176 (2010), pp. 285-306

[4] Lalonde, F.; Pestieau, C. Stabilization of symplectic inequalities and applications, Amer. Math. Soc. Transl., Volume 196 (1999), pp. 63-72

[5] Lalonde, F.; Polterovich, L. Symplectic diffeomorphisms as isometries of Hoferʼs norm, Topology, Volume 36 (1997), pp. 711-727

[6] McDuff, D.; Salamon, D. Introduction to Symplectic Topology, Oxford University Press, 1994

[7] Polterovich, L. The Geometry of the Group of Symplectic Diffeomorphisms, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, 2001

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