Let $G$ and $H$ be Lie groups and let $G\rtimes H$ be the product $G\times H$ with group structure given by $$(g_1,h_1)\cdot (g_2,h_2)=(g_1\cdot(h_1g_2),h_1h_2)$$ (i.e. the semi-direct product group). Why is $EH\times_H BG$ a model for $B(G\rtimes H)$?
2026-03-27 16:47:37.1774630057
Classifying space of semi-direct product of Lie groups
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