scholarly journals The homeomorphism group of the first uncountable ordinal

2021 ◽  
Vol 67 (1) ◽  
pp. 145-159
Author(s):  
Maxime Gheysens
Keyword(s):  
Homeomorphism Group

scholarly journals CONFIGURATION CATEGORIES AND HOMOTOPY AUTOMORPHISMS

2018 ◽  
Vol 62 (1) ◽  
pp. 13-41
Author(s):  
MICHAEL S. WEISS
Keyword(s):  
Compact Manifold ◽  
Geometric Conditions ◽  
Homeomorphism Group ◽  
Manifold With Boundary ◽  
Smooth Compact Manifold

AbstractLet M be a smooth compact manifold with boundary. Under some geometric conditions on M, a homotopical model for the pair (M, ∂M) can be recovered from the configuration category of M \ ∂M. The grouplike monoid of derived homotopy automorphisms of the configuration category of M \ ∂M then acts on the homotopical model of (M, ∂M). That action is compatible with a better known homotopical action of the homeomorphism group of M \ ∂M on (M, ∂M).

scholarly journals The universal minimal flow of the homeomorphism group of the Lelek fan

2018 ◽  
Vol 371 (10) ◽  
pp. 6995-7027 ◽  
Author(s):  
Dana Bartošová ◽  
Aleksandra Kwiatkowska
Keyword(s):  
Minimal Flow ◽  
Homeomorphism Group

scholarly journals Compactifications of the homeomorphism group of a graph

2010 ◽  
Vol 157 (6) ◽  
pp. 1044-1063
Author(s):  
Atsushi Yamashita
Keyword(s):  
Homeomorphism Group

scholarly journals UNIVERSAL MINIMAL FLOWS OF GENERALIZED WAŻEWSKI DENDRITES

2018 ◽  
Vol 83 (04) ◽  
pp. 1618-1632 ◽  
Author(s):  
ALEKSANDRA KWIATKOWSKA
Keyword(s):  
Minimal Flow ◽  
Topological Groups ◽  
Homeomorphism Group ◽  
Image Position ◽  
Homeomorphism Groups

AbstractWe study universal minimal flows of the homeomorphism groups of generalized Ważewski dendrites WP, $P \subseteq \left\{ {3,4, \ldots ,\omega } \right\}$. If P is finite, we prove that the universal minimal flow of the homeomorphism group H (WP) is metrizable and we compute it explicitly. This answers a question of Duchesne. If P is infinite, we show that the universal minimal flow of H (WP) is not metrizable. This provides examples of topological groups which are Roelcke precompact and have a nonmetrizable universal minimal flow with a comeager orbit.

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