Topological realizations of groups in Alexandroff spaces

2019/07/12 by Pedro J. Chocano, Chocano, P. J., Manuel A. Morón +3 · 2 citations
Computer Science · Mathematics · #Topological and Geometric Data Analysis #Homotopy and Cohomology in Algebraic Topology #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.1907.05654

Abstract

We prove that every group can be realized as the homeomorphism group and as the group of (pointed) homotopy classes of (pointed) self-homotopy equivalences of infinitely many non-homotopy-equivalent Alexandroff spaces.

Cited by

• Every group retraction can be realized as a topological retraction
• Riordan pattern's quest within simplicial complexes

Related

• On some topological realizations of groups and homomorphisms
• A Short Study of Alexandroff Spaces
• On homotopy types of Alexandroff spaces
• Regular coverings and fundamental groupoids of Alexandroff spaces
• On continuous homomorphisms from Alexandroff paratopological groups into topological groups