|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
Exotic Dehn twists on
sums of two contact $3$-manifolds
Eduardo Fernández and Juan Muñoz-Echániz |
|
Geometry & Topology 29 (2025) 1571–1618
|
 |
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 -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 -principle for families of convex spheres in tight contact -manifolds, from which we establish a parametric version of Colin’s decomposition theorem. As a further application, we exhibit new exotic -parametric phenomena in overtwisted contact -manifolds. |
Keywords
contact structures on 3-manifolds, contactomorphisms, Dehn
twist, monopole Floer homology
|
Mathematical Subject Classification
Primary: 53D35, 57K33, 57R58
|
References |
Publication
Received: 3 July 2023
Revised: 9 April 2024
Accepted: 27 July 2024
Published: 31 May 2025
Proposed: Yakov Eliashberg
Seconded: Ciprian Manolescu, Leonid Polterovich
|
Authors |
| Eduardo Fernández | |
| Mathematics Department University of Georgia Athens, GA United States |
|
| Juan Muñoz-Echániz | |
| Department 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 |
| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
Open Access made possible by participating institutions via Subscribe to Open.
