2019/03/17 by Yoshihiro Sugimoto, Sugimoto, Yoshihiro
Computer Science · Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1903.07055
openalex publication_date 2019/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove that on any contact manifold, 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 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.