All Questions

The classifying space $BS^1$ for $S^1$-bundles can be taken to be the colimit of $\mathbb{CP}^n$ which are smooth manifolds and the inclusions $\mathbb{CP}^n \hookrightarrow \mathbb{CP}^{n+1}$ are ...

Two questions (more details below): Let $G$ be a compact Lie group and $X$ a $G$-space such that all stabilizer subgroups are conjugate to a fixed $H \leq G$. Denote by $\pi: X \to X/G$ the quotient ...

Let $G$ be a compact Lie group and $V$ a finite-dimensional orthogonal $G$-representation. Write $S^V$ for the quotient $D(V)/S(V)$, where $D(V)$ and $S(V)$ are the unit disk and sphere in $V$, ...