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In this chapter we state the Quotient Manifold Theorem, which tells us that the quotient space of a smooth proper free action is naturally a smooth manifold. We use this to define homogeneous spaces. Finally we investigate the adjoint representation of a Lie group.

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Homogeneous Spaces

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  • 发表日期：

    2026年

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  • Will J. Merry

摘要

In this chapter we state the Quotient Manifold Theorem, which tells us that the quotient space of a smooth proper free action is naturally a smooth manifold. We use this to define homogeneous spaces. Finally we investigate the adjoint representation of a Lie group.