Growth of maps, distortion in groups and symplectic geometry

Research output: Contribution to journalArticlepeer-review

Abstract

In the present paper we study two sequences of real numbers associated to a symplectic diffeomorphism: • The uniform norm of the differential of its n-th iteration; • The word length of its n-th iteration, where we assume that our diffeomorphism lies in a finitely generated group of symplectic diffeomorphisms. We find lower bounds for the growth rates of these sequences in a number of situations. These bounds depend on the symplectic geometry of the manifold rather than on the specific choice of a diffeomorphism. They are obtained by using recent results of Schwarz on Floer homology. As an application, we prove non-existence of certain non-linear symplectic representations for finitely generated groups.

Original languageEnglish
Pages (from-to)655-686
Number of pages32
JournalInventiones Mathematicae
Volume150
Issue number3
DOIs
StatePublished - 2002

Fingerprint

Dive into the research topics of 'Growth of maps, distortion in groups and symplectic geometry'. Together they form a unique fingerprint.

Cite this