The homeomorphism group of the universal Knaster continuum

2022/08/04 by Sumun Iyer, Iyer, Sumun · 1 citation
Mathematics · #03C98 (Secondary) #03E15 (Primary) 54F15 #05D10 #37B05 #Advanced Topology and Set Theory #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Logic (math.LO) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2208.02461

openalex publication_date 2022/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a projective Fraissé family whose limit approximates the universal Knaster continuum. The family is such that the group \textrmAut(\mathbbK) of automorphisms of the Fraissé limit is a dense subgroup of the group, \textrmHomeo(K), of homeomorphisms of the universal Knaster continuum. We prove that both \textrmAut(\mathbbK) and \textrmHomeo(K) have universal minimal flow homeomorphic to the universal minimal flow of the free abelian group on countably many generators. The computation involves proving that both groups contain an open, normal subgroup which is extremely amenable.

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