On Sandon-type metrics for contactomorphism groups
Symplectic Geometry
2016-10-28 v2
Abstract
For certain contact manifolds admitting a 1-periodic Reeb flow we construct a conjugation-invariant norm on the universal cover of the contactomorphism group. With respect to this norm the group admits a quasi-isometric monomorphism of the real line. The construction involves the partial order on contactomorphisms and symplectic intersections. This norm descends to a conjugation-invariant norm on the contactomorphism group. As a counterpoint, we discuss conditions under which conjugation-invariant norms for contactomorphisms are necessarily bounded.
Cite
@article{arxiv.1207.3151,
title = {On Sandon-type metrics for contactomorphism groups},
author = {Maia Fraser and Leonid Polterovich and Daniel Rosen},
journal= {arXiv preprint arXiv:1207.3151},
year = {2016}
}
Comments
32 pages. Expanded and updated version. Section 2.4 is new material not appearing in previous version, other section numbers have changed