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3 votes
1 answer
454 views

Principal bundles from a fibration of homogeneous spaces

Let $G$ be a compact (Lie) group, and $H \subseteq H'$ two compact (Lie) subgroups. It is clear that we have an obvious surjective map of homogeneous spaces $$ G/H \twoheadrightarrow G/H'. $$ Will it ...
4 votes
1 answer
384 views

Invariant integration on principal bundles

Let $G$ be a sufficiently nice topological or Lie group (e.g. compact), and let $H$ be a closed subgroup. This data determines a principal $H$ bundle $G \rightarrow G/H$ defined by the projection $g \...