Exotic Dehn twists on sums of two contact 3-manifolds

Fernández, Eduardo¹ ; Muñoz-Echániz, Juan²

¹Mathematics Department, University of Georgia, Athens, GA, United States
²Department of Mathematics, Columbia University, New York, NY, United States, Simons Center for Geometry and Physics, State University of New York, Stony Brook, Stony Brook, NY, United States

Geometry & topology, Tome 29 (2025) no. 3, pp. 1571-1618

Résumé

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. We make essential use of an invariant for families of contact structures which generalizes 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 exhibit new exotic 1-parametric phenomena in overtwisted contact 3-manifolds.

Détail

DOI : 10.2140/gt.2025.29.1571

Keywords: contact structures on 3-manifolds, contactomorphisms, Dehn twist, monopole Floer homology

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