Bott-integrability of overtwisted contact structures

Abstract

We show that an overtwisted contact structure on a closed, oriented 3-manifold can be defined by a contact form having a Bott-integrable Reeb flow if and only if the Poincaré dual of its Euler class is represented by a graph link.

19 pages, 1 figure; v2: added Remark 1.3 and some references