Adam Przezdziecki, Uniwersytet Warszawski Model category

Adam Przezdziecki, Uniwersytet Warszawski
Model category structure on topogenic groups
Abstract: A topogenic group is a pair (G, P ), where G is a discrete group and P is its
normal perfect subgroup. We describe a model category structure on the category of topogenic
groups such that the Quillen +construction on BG with respect to P yields an equivalence
between the corresponding homotopy category and the homotopy category of pointed connected
CW-complexes.
This category was introduced by A. Heller [1] where he suggested that it does not admit such a
model structure.
• [1] Alex Heller, On the homotopy theory of topogenic groups and groupoids. Illinois J.
Math. 24 (1980), n. 4, 576–605.
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