2024/01/26 by Pierre Cagne, Cagne, Pierre, Ulrik Buchholtz +5
Engineering · Mathematics · #03B38 (Secondary) #55P10 (Primary) 55U40 #Advanced Materials and Mechanics #Algebraic Topology (math.AT) #F.4.1 #FOS: Computer and information sciences #FOS: Mathematics #Geometric and Algebraic Topology #Logic in Computer Science (cs.LO) #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.2401.15037
openalex publication_date 2024/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Working in univalent foundations, we investigate the symmetries of spheres, i.e., the types of the form \mathbbSn = \mathbbSn. The case of the circle has a slick answer: the symmetries of the circle form two copies of the circle. For higher-dimensional spheres, the type of symmetries has again two connected components, namely the components of the maps of degree plus or minus one. Each of the two components has ℤ/2ℤ as fundamental group. For the latter result, we develop an EHP long exact sequence.