TL;DR
This paper introduces a contact analog of the symplectic cut construction and demonstrates its application in showing the existence of many nonconjugate tori within the contactomorphism group of an overtwisted three-sphere.
Contribution
It presents a novel contact cut construction and applies it to analyze the structure of the contactomorphism group in overtwisted contact 3-manifolds.
Findings
Existence of countably many nonconjugate two tori in the contactomorphism group
Development of a contact analog of the symplectic cut construction
Application to overtwisted contact structures on the three sphere
Abstract
We describe a contact analog of the symplectic cut construction. As an application we show that the group of contactomorphisms for a particular overtwisted contact structure on the three sphere contains countably many nonconjugate two tori.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · semigroups and automata theory