Pinwheels and bypasses (Q2571366)

This paper builds upon earlier work by the authors concerning tight contact structures on 3--manifolds. Here they consider the question as to when the attachment of a family of bypasses along a family of Legendrian curves to a convex surface results in a tight contact manifold. (The attachment of bypasses was introduced by \textit{K. Honda} in [Geom. Topol. 4, 309--368 (2000; Zbl 0980.57010)]). The answer is that a necessary and sufficient condition for this to happen is the nonexistence of a polygonal region which they call a virtual pinwheel.