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Axioms 2019, 8(2), 43; https://doi.org/10.3390/axioms8020043

Applications of Square Roots of Diffeomorphisms

Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
Received: 9 March 2019 / Revised: 8 April 2019 / Accepted: 9 April 2019 / Published: 11 April 2019
(This article belongs to the Special Issue Fixed Point Theory and Related Topics)
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Abstract

In this paper, we prove that on any contact manifold ( M , ξ ) there exists an arbitrary C -small contactomorphism which does not admit a square root. In particular, there exists an arbitrary C -small contactomorphism which is not “autonomous”. This paper is the first step to study the topology of C o n t 0 ( M , ξ ) Aut ( M , ξ ) . As an application, we also prove a similar result for the diffeomorphism group Diff ( M ) for any smooth manifold M. View Full-Text
Keywords: diffeomorphism; contactomorphism; symplectomorphism diffeomorphism; contactomorphism; symplectomorphism
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Sugimoto, Y. Applications of Square Roots of Diffeomorphisms. Axioms 2019, 8, 43.

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