Date of Award
Spring 2015
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
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.
Recommended Citation
Weigel, Peter, "Orderability and rigidity in contact geometry" (2015). Open Access Dissertations. 589.
https://docs.lib.purdue.edu/open_access_dissertations/589