Examples of non-trivial contact mapping classes in all dimensions
Patrick Massot, Klaus Niederkr\"uger
TL;DR
This paper constructs examples of contactomorphisms in all dimensions that are smoothly isotopic but not contact or symplectically pseudo-isotopic to the identity, revealing new complexities in contact topology.
Contribution
It provides the first known examples of contactomorphisms that are smoothly isotopic but not contact or symplectically pseudo-isotopic to the identity in all dimensions.
Findings
Existence of contactomorphisms not contact isotopic to the identity
Examples of smoothly conjugate contactomorphisms not related by contactomorphisms
Demonstration of non-trivial contact mapping classes
Abstract
We give examples of contactomorphisms in every dimension that are smoothly isotopic to the identity but that are not contact isotopic to the identity. In fact, we prove the stronger statement that they are not even symplectically pseudo-isotopic to the identity. We also give examples of pairs of contactomorphisms which are smoothly conjugate to each other but not by contactomorphisms.
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