Finite symmetries of S⁴

2014/12/18 by Weimin Chen, Slawomir Kwasik, Chen, Weimin +4
Mathematics · #19J25 #57R67 #57S05 #57S17 (primary) #57S25 (secondary) #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:19J25 #msc:57R67 #msc:57S05 #msc:57S17 #msc:57S25

paper · pdf · doi:10.48550/arxiv.1412.5901

23 pages, no figures, accepted by Forum Mathematicum

arxiv created 2014/12/18 · openalex publication_date 2014/12/18 · arxiv updated 2014/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

This paper discusses topological and locally linear actions of finite groups on S⁴. Local linearity of the orientation preserving actions on S⁴ forces the group to be a subgroup of SO(5). On the other hand, orientation reversing topological actions of "exotic" groups G (i.e. G\not⊂ O(5)) on S⁴ are constructed, and local linearity and stable smoothability of the actions are studied.

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