Date of Award

Spring 2015

Degree Type


Degree Name

Doctor of Philosophy (PhD)



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


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.

Included in

Mathematics Commons