All Questions
2 questions
3
votes
0
answers
134
views
When do quotients of $G$-vector bundles exist?
Let's work in the category of smooth (paracompact, Hausdorff) manifolds. Let $M$ be a manifold and $G$ a Lie group acting on $M$. Suppose $E$ is a $G$-vector bundle on $M$ (that is, $G$ acts on $E$ by ...
- 51
3
votes
1
answer
105
views
Define a symplectic structure on $G \times_{G_\beta} V$, where $V$ is symplectic
Let $G$ be a compact Lie group with algebra $\mathfrak{g}$. Let $\beta $ be an element in the dual of the Lie algebra $\mathfrak{g}$. We denote by $G_\beta$ the stabilizer subgroup of $\beta$ by ...
- 139