Comptes Rendus
no. 19-20
Differential Geometry
On the bounded isometry conjecture
[Sur la conjecture dʼisométrie bornée]

Présenté par : the Editorial Board

Andrés Pedroza1
1 Facultad de Ciencias, Universidad de Colima, Bernal Díaz del Castillo No. 340, Colima, Col., Mexico 28045
Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1097-1100.

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

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

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.08.016
Andrés Pedroza 1

1 Facultad de Ciencias, Universidad de Colima, Bernal Díaz del Castillo No. 340, Colima, Col., Mexico 28045 
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     title = {On the bounded isometry conjecture},
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     pages = {1097--1100},
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     doi = {10.1016/j.crma.2011.08.016},
     language = {en},
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Andrés Pedroza. On the bounded isometry conjecture. Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1097-1100. doi : 10.1016/j.crma.2011.08.016. https://comptes-rendus.academie-sciences.fr/mathematique/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] Z. Han Bi-invariant metrics on the group of symplectomorphisms, Trans. Amer. Math. Soc., Volume 361 (2009), pp. 3343-3357

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

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

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

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

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

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