%0 Journal Article %A Girish Kulkarni %A Matthias Wendt %A Elden Elmanto %T $\mathbb{A}^1$-connected components of classifying spaces and purity for torsors %J Documenta mathematica %D 2022 %P 2657-2689 %V 27 %U http://geodesic.mathdoc.fr/articles/10.4171/dm/x38/ %R 10.4171/dm/x38 %F 10_4171_dm_x38