Realizations of countable groups as fundamental groups of compacta

DOI10.1007/s00009-013-0274-0zbMath1279.55009arXiv0810.3412OpenAlexW2153255278MaRDI QIDQ358267

Žiga Virk

Publication date: 16 August 2013

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.3412

zbMATH Keywords

fundamental groupEilenberg-MacLane spacePeano continuumcompactacountable grouphomotopical closenessthe realization theorem

Mathematics Subject Classification ID

Homotopy groups, general; sets of homotopy classes (55Q05) Topological methods in group theory (57M07) Compact (locally compact) metric spaces (54E45) Fundamental group, presentations, free differential calculus (57M05) Eilenberg-Mac Lane spaces (55P20)

Related Items (3)

Embeddings of locally compact abelian \(p\)-groups in Hawaiian groups ⋮ Homotopical smallness and closeness ⋮ EVERY COUNTABLE GROUP IS THE FUNDAMENTAL GROUP OF SOME COMPACT SUBSPACE OF

Cites Work

• Small loop spaces
• Homotopy, simple homotopy and compacta
• The combinatorial structure of the Hawaiian earring group
• On the fundamental groups of one-dimensional spaces
• Covering maps for locally path-connected spaces
• An alternate proof that the fundamental group of a Peano continuum is finitely presented if the group is countable
• Measurable cardinals and fundamental groups of compact spaces
• On fundamental groups of compact Hausdorff spaces
• Can the Fundamental (Homotopy) Group of a Space be the Rationals?
• The fundamental group of a compact metric space

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