Universal minimal flows from a homotopical perspective

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Dátum

2026

Názov časopisu

ISSN časopisu

Názov zväzku

Vydavateľ

Springer-Verlag : Heidelberg

ISBN

ISSN

0025-5874
1432-1823

Abstrakt

We study universal minimal flows of connected and locally contractible topological groups by means of tools from homotopy theory and dynamical cohomology. We provide methods for computing their first cohomotopy groups and illustrate them by computations related to connected Lie groups and identity components of homeomorphism groups of compact connected surfaces with or without boundary. Since metrizable spaces have countable first cohomotopy groups, these methods serve as a useful new instrument for proving nonmetrizability of various universal minimal flows. In this way we reprove several results in this direction known before and also prove some new ones. Finally, we indicate how our methods can be used to construct finite-dimensional minimal spaces for infinite-dimensional topological groups, having all orbits of first category.

Popis

In: Mathematische Zeitschrift. Heidelberg : Springer-Verlag, 2026. ISSN 0025-5874. Vol. 312, no. 1 (2026), art. no. 29, pp. [1-38].

Kľúčové slová

minimálny tok, univerzálny minimálny tok, universal minimal flow, dynamické kohomológie, dynamic cohomologies, kohomotopické grupy, cohomological groups

Výstup z projektu

VEGA 1/0634/24 Dynamika: minimálnosť, chaos, rekurentnosť

Citácia

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CC BY Creative Commons Attribution 4.0. International
info:eu-repo/semantics/openAccess