Pseudo-distances on symplectomorphism groups and applications to flux theory

Details Pseudo-distances on symplectomorphism groups and applications to flux theory Pseudo-distances on symplectomorphism groups and applications to flux theory

Publishing date

2011-03-26

URL

arxiv.org/abs/1103.5144v1

Science

Mathematics

Field

Symplectic Geometry

Additional info

20 pages, no figure

Type

Scientific paper

Abstract

Starting from a given norm on the vector space of exact 1-forms of a compact symplectic manifold, we produce pseudo-distances on its symplectomorphism group by generalizing an idea due to Banyaga. We prove that in some cases (which include Banyaga's construction), their restriction to the Hamiltonian diffeomorphism group is equivalent to the distance induced by the initial norm on exact 1-forms. We also define genuine "distances to the Hamiltonian diffeomorphism group" which we use to derive several consequences, mainly in terms of flux groups.

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