All Questions

Let a compact Lie group $G$ act smoothly on a compact smooth manifold $M$. For any compact subgroup $H\subset G$ denote by $E^H$ the image in $M/G$ of the fixed point set of $H$ in $M$. Is it true ...

Let $M$ be a smooth manifold and let $G$ be a compact Lie group acting smoothly and freely over $M$. Let $\pi:M\rightarrow M/G$ be the canonical projection, and endow $M/G$ with the unique ...

$\DeclareMathOperator\SO{SO}$Say I have coordinates for $\SO(3,\mathbb{R})$, e.g., a parametrization by Euler angles. Is there a reasonable way to explicitly prescribe coordinates on the quotient ...

Let $M$ be a smooth finite dimensional manifold, how restrictive is it to require $M$ to admit a smooth action by a finite dimensional Lie group $G$? Related questions/approaches: Of course we need $\...