Crossed modules as maps between connected components of topological groups

Emmanuel D. Farjoun, Yoav Segev

Research output: Contribution to journalArticlepeer-review

Abstract

The purpose of this paper is to observe that a homomorphism of discrete groups f : Γ → G arises as the induced map π 0 (M) → π 0 (M) on path components of some closed normal inclusion of topological groups M ⊂ M if and only if the map f can be equipped with a crossed module structure. In that case an essentially unique realization M M exists by homotopically discrete topological groups. The results here are topological elaboration and exposition using existing simplicial techniques.

Original languageEnglish
Pages (from-to)1463-1469
Number of pages7
JournalForum Mathematicum
Volume29
Issue number6
DOIs
StatePublished - 1 Nov 2017

Keywords

  • Crossed module
  • connected components
  • normal map
  • topological group

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