Examples of contact mapping classes of infinite order in all dimensions
Fabio Gironella
TL;DR
This paper presents examples of high-dimensional contact manifolds with contactomorphisms of infinite order, where all powers are smoothly isotopic but not contact-isotopic, extending known 3D phenomena to higher dimensions.
Contribution
It generalizes the phenomenon of contactomorphisms of infinite order from 3D to all higher dimensions, providing new examples in contact topology.
Findings
Existence of high-dimensional contact manifolds with infinite order contactomorphisms
All powers of these contactomorphisms are smoothly isotopic to identity
Powers are not contact-isotopic to the identity
Abstract
We give examples of tight high dimensional contact manifolds admitting a contactomorphism whose powers are all smoothly isotopic but not contact-isotopic to the identity. This is a generalization of an observation in dimension 3 by Gompf, also reused by Ding and Geiges.
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