Abstract
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.
Disciplines
Mathematics
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
First Advisor
Peter Albers
Second Advisor
Laszlo Lempert
Committee Chair
Peter Albers
Committee Co-Chair
Laszlo Lempert
Committee Member 1
Steve Bell
Committee Member 2
Ralph Kaufmann
Date of Award
Spring 2015
Recommended Citation
Weigel, Peter, "Orderability and rigidity in contact geometry" (2015). Open Access Dissertations. 589.
https://docs.lib.purdue.edu/open_access_dissertations/589