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8 pages, 220 KB

Open AccessArticle

by Yoshihiro Sugimoto

Axioms 2019, 8(2), 43; https://doi.org/10.3390/axioms8020043 - 11 Apr 2019

Viewed by 2753

In this paper, we prove that on any contact manifold

(M, ξ)

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 [...] Read more.

In this paper, we prove that on any contact manifold

(M, ξ)

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 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. Full article

(This article belongs to the Special Issue Fixed Point Theory and Related Topics)

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