Journal of Symplectic Geometry

Volume 13 (2015)

Number 2

Orderable contact structures on Liouville-fillable contact manifolds

Pages: 463 – 496



Peter Weigel (Department of Mathematics, Purdue University, West Lafayette, Indiana, U.S.A.)


We study the existence of positive loops of contactomorphisms on a Liouville-fillable contact manifold $(\Sigma, \xi = \ker (\alpha))$. Previous results (see [6]) show that a large class of Liouville-fillable contact manifolds admit contractible positive loops. In contrast, we show that for any Liouville-fillable $(\Sigma, \alpha)$ with $\dim (\Sigma) \geq 7 \,$ there exists a Liouville-fillable contact structure $\xi^\prime$ on $\Sigma$ which admits no positive loop at all. Further, $\xi^\prime$ can be chosen to agree with $\xi$ on the complement of a Darboux ball.

Published 13 April 2015