Topological contact dynamics I: symplectization and applications of the energy-capacity inequality
-
Stefan Müller
and
Peter Spaeth
Abstract
We introduce topological contact dynamics of a smooth manifold carrying a cooriented contact structure, generalizing previous work in the case of a symplectic structure [27] or a contact form [5]. A topological contact isotopy is not generated by a vector field; nevertheless, the group identities, the transformation law, and classical uniqueness results in the smooth case extend to topological contact isotopies and homeomorphisms, giving rise to an extension of smooth contact dynamics to topological dynamics. Our approach is via symplectization of a contact manifold, and our main tools are an energy-capacity inequality we prove for contact diffeomorphisms, combined with techniques from measure theory on oriented manifolds. We establish non-degeneracy of a Hofer-like bi-invariant pseudo-metric on the group of strictly contact diffeomorphisms constructed in [4]. The topological automorphism group of the contact structure exhibits rigidity properties analogous to those of symplectic diffeomorphisms, including C0-rigidity of contact and strictly contact diffeomorphisms.
© 2015 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- A natural extension of the Young partition lattice
- Pencils of small degree on curves on unnodal Enriques surfaces
- Michael’s Selection Theorem in a semilinear context
- Quasi-simple Lie groups as multiplication groups of topological loops
- Some spectral results on Kakeya sets
- Projective normality and the generation of the ideal of an Enriques surface
- Topological contact dynamics I: symplectization and applications of the energy-capacity inequality
- Torsion-free G*2(2)-structures with full holonomy on nilmanifolds
Articles in the same Issue
- Frontmatter
- A natural extension of the Young partition lattice
- Pencils of small degree on curves on unnodal Enriques surfaces
- Michael’s Selection Theorem in a semilinear context
- Quasi-simple Lie groups as multiplication groups of topological loops
- Some spectral results on Kakeya sets
- Projective normality and the generation of the ideal of an Enriques surface
- Topological contact dynamics I: symplectization and applications of the energy-capacity inequality
- Torsion-free G*2(2)-structures with full holonomy on nilmanifolds
