Exotic Dehn twists on sums of two contact 3-manifolds

Abstract

We exhibit the first examples of exotic contactomorphisms with infinite order as elements of the contact mapping class group. These are given by certain Dehn twists on the separating sphere in a connected sum of two closed contact 3-manifolds. We detect these by a combination of hard and soft techniques. On the one hand, we make essential use of an invariant for families of contact structures which generalises the Kronheimer--Mrowka contact invariant in monopole Floer homology. We then exploit an h-principle for families of convex spheres in tight contact 3-manifolds, from which we establish a parametric version of Colin's decomposition theorem. As a further application, we also exhibit new exotic 1-parametric phenomena in overtwisted contact 3-manifolds.

Final version; accepted in Geometry & Topology

References in corpus (2)

• Isotopy of the Dehn twist on K3#K3 after a single stabilization
• A monopole invariant for families of contact structures