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Is the manifold of complex points of a quotient of compact groups just the tangent bundle?
In great generality a Lie group mod its maximal compact subgroup is contractible (for example this is true for all connected Lie groups). Whenever this is true then the Lie group $ D $ is ...
- 4,081
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Is a quotient of real linear algebraic groups always a Cartesian product of compact and contractible factors?
Let $ G $ be the real points of a linear algebraic group and $ G' $ a Zariski closed subgroup. Then is $ G/G' $ a Cartesian product
$$
(K/K') \times F
$$
where $ F $ is contractible? Here $ K,K' $ ...
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