%0 Journal Article %A Elmanto, Elden %A Kulkarni, Girish %A Wendt, Matthias %T \(\mathbb{A}^1\)-connected components of classifying spaces and purity for torsors %J Documenta mathematica %D 2022 %P 2657-2689 %V 27 %I mathdoc %U http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a1/ %G en %F DOCMA_2022__27__a1