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arXiv · 1903.07055

Applications of square roots of diffeomorphisms

Yoshihiro Sugimoto
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Abstract

In this paper, we prove that on any contact manifold, there exists an arbitrary C^{\infty}-small contactomorphism which does not admit a square root. In particular, there exists an arbitrary C^{\infty}-small contactomorphism which is not "autonomous". This result is the first step to study the topology of non-autonomous contactomorphisms. As an application, we also prove a similar result for the diffeomorphism group for any smooth manifold.

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Yoshihiro Sugimoto. 2019-03-17. Applications of square roots of diffeomorphisms. https://arxiv.org/abs/1903.07055

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