A group of isometries with non-closed orbits

2009/10/25 by Herbert Abels, Abels, Herbert, Antonios Manoussos +1
Mathematics · #37B05 #54H15 #54H20 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN) #Geometric and Algebraic Topology #math.DS #math.GN #msc:37B05 #msc:54H15 #msc:54H20

paper · pdf · doi:10.48550/arxiv.0910.4717

4 pages

arxiv created 2009/10/25 · openalex publication_date 2009/10/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we give an example of a one-dimensional manifold with two connected components and a complete metric whose group of isometries has an orbit which is not closed. This answers a question of S. Gao and A. S. Kechris.

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