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 language | English |
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Pages (from-to) | 1463-1469 |
Number of pages | 7 |
Journal | Forum Mathematicum |
Volume | 29 |
Issue number | 6 |
DOIs | |
State | Published - 1 Nov 2017 |
Bibliographical note
Publisher Copyright:© 2017 Walter de Gruyter GmbH, Berlin/Boston 2017.
Keywords
- connected components
- Crossed module
- normal map
- topological group