On the bounded isometry conjecture

Andrés Pedroza

doi:10.1016/j.crma.2011.08.016

Differential Geometry

On the bounded isometry conjecture

Presented by: 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.

Abstract
Résumé

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.

Received: 2011-02-15
Accepted: 2011-08-22
Published online: 2011-09-15

DOI: 10.1016/j.crma.2011.08.016

Author's affiliations:

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},
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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/

References
Cited by

[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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