Orderability and rigidity in contact geometry

<p>We study the existence of positive loops of contactomorphisms on a Liouville-fillable contact manifold (&Sgr;, ξ = ker(α)). Previous results (see [1]) show that a large class of Liouville-fillable contact manifolds admit contractible positive loops. In contrast, we show that for any Liouville-fillable (&Sgr;, α) with dim(&Sgr;) ≥ 7, there exists a Liouville-fillable contact structure ξ' on &Sgr; which admits no positive loop at all. Further, ξ' can be chosen to agree with ξ' on the complement of a Darboux ball. We then define a relative version of orderability for a Legendrian submanifold, and discuss the relationship between the two notions.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Year

2015

Author dc:creator

• Weigel, Peter

Contributors dc:contributor

• Peter Albers
• Laszlo Lempert
• Steve Bell
• Ralph Kaufmann

• Mathematics

Repository record dc:identifier

https://docs.lib.purdue.edu/open_access_dissertations/589

OAI identifier oai:identifier

oai:docs.lib.purdue.edu:open_access_dissertations-1570