All Questions

Every smooth manifold is assumed to be Hausdorff and second-countable. Suppose $G$ is a Lie group, $H$ is a Lie subgroup of $G$, $N$ is a closed Lie subgroup of $G$ such that $N$ is normal, $N\cap H=\...

Let $G$ be a Lie group and $H$ a Lie subgroup of $G$. Let $M$ be a smooth manifold. Let $\theta$ be a left smooth action of $G$ on $M$. Let $S=\{p\in M| G_p=H\}$, where $G_p$ is the isotropy ...

Let $G$ be a Lie group acting smoothly and freely on a smooth manifold $M$. Suppose that the quotient space $M/G$ is a topological manifold. Do we have $$\dim(M/G)=\dim M-\dim G?$$ Notes: This ...

Let $M$ be a connected smooth manifold, and assume that it is parallelisable; that is, its tangent bundle is trivial. Does $M$ admit an H space structure? That is, does there exist a smooth map $\mu:...

I'm trying to better understand the manifold GL+(3,R)/S0(3) which is diffeomorphic to positive definite symmetric matrices. My motivation is to understand U in F = RU where F in GL+(3,R) = deformation ...