2021/02/23 by Iván Sadofschi Costa, Costa, Iván Sadofschi
Computer Science · Mathematics · #57M60 #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2102.11458
openalex publication_date 2021/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this series of two articles, we prove that every action of a finite group G on a finite and contractible 2-complex has a fixed point. The proof goes by constructing a nontrivial representation of the fundamental group of each of the acyclic 2-dimensional G-complexes constructed by Oliver and Segev. In the first part we develop the necessary theory and cover the cases where G=PSL2(2n), G=PSL2(q) with q≡ 3\pmod 8 or G=Sz(2n). The cases G=PSL2(q) with q≡ 5\pmod 8 are addressed in the second part.