On the bounded isometry conjecture

Andrés Pedroza

doi:10.1016/j.crma.2011.08.016

Differential Geometry

On the bounded isometry conjecture
[Sur la conjecture dʼisométrie bornée]

Présenté par : the Editorial Board

Andrés Pedroza ¹

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.

Résumé
Abstract

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 : 2011-02-15
Accepté le : 2011-08-22
Publié le : 2011-09-15

DOI : 10.1016/j.crma.2011.08.016

Affiliations des auteurs :

Andrés Pedroza ¹

¹ Facultad de Ciencias, Universidad de Colima, Bernal Díaz del Castillo No. 340, Colima, Col., Mexico 28045

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     author = {Andr\'es Pedroza},
     title = {On the bounded isometry conjecture},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1097--1100},
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     number = {19-20},
     year = {2011},
     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/

Bibliographie
Cité par

[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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