Work

Exotic Dehn twists on sums of two contact 3-manifolds

Year: 2025

Type: article

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.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.

Source: Geometry & Topology

DOI: 10.2140/gt.2025.29.1571

Authors: Eduardo Fernández, Juan Muñoz-Echániz

Institutions: University of Georgia, Simons Center for Geometry and Physics, Stony Brook University, Columbia University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: National Science Foundation

Award: New Directions in Monopole Floer Homology