2018/03/22 by Xiaotian Pan, Pan, Xiaotian, Bingzhe Hou +1 · 1 citation
Mathematics · #22C05 #37C15 #55S37 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Dynamical Systems (math.DS) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #math.DS #msc:22C05 #msc:37C15 #msc:55S37
paper · pdf · doi:10.48550/arxiv.1803.08430
50 pages. Accepted for publication in SCIENCE CHINA Mathematics
openalex publication_date 2018/03/22 · openalex created_date 2018/03/29 · arxiv created 2019/04/29 · arxiv updated 2019/04/30 · openalex updated_date 2026/07/28
In this article, we focus on the left translation actions on noncommutative compact connected Lie groups with topological dimension 3 or 4, consisting of \rm SU(2), \rm U(2), \rm SO(3), \rm SO(3) × S1 and \rm Spinℂ(3). We define the rotation vectors (numbers) of the left actions induced by the elements in the maximal tori of these groups, and utilize rotation vectors (numbers) to give the topologically conjugate classification of the left actions. Algebraic conjugacy and smooth conjugacy are also considered. As a by-product, we show that for any homeomorphism f:L(p, -1)× S1→ L(p, -1)× S1, the induced isomorphism (π∘ f∘ i)_* maps each element in the fundamental group of L(p, -1) to itself or its inverse, where i:L(p,-1)→ L(p, -1)× S1 is the natural inclusion and π:L(p, -1)× S1→ L(p, -1) is the projection.