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7 votes
1 answer
221 views

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' $ ...
1 vote
1 answer
345 views

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 ...