MathOverflow

I have a closed (compact without boundary) manifold M and a compact Lie group G that acts on it. I wan't to understand the topology of $M/G$, at least compute its singular homology groups. The action isn't free, so $M/G$ may not be a manifold. Because...

TL;DR version: With the magician's back turned, a spectator shuffles a standard deck of $n=52$ playing cards and selects and arranges $m=27$ of them face-up in a row left to right. The magician's assistant turns one of these cards face-down, leaving...

Okay, loosely speaking, a homeomorphism is a continuous, bijective, and invertible mapping. A homotopy is a continuous deformation of a topological space with a parameter. An isotopy is a homotopy that is a homeomorphism in the interval from 0 to 1....

Let $G=(V,E)$ be a simple graph and $\Phi:=\lbrace \phi\rbrace$ a set of cycles such that for every edge $e\in E$ there is a $\phi\in \Phi$ such that $e\in \phi$. We say that $\Phi$ covers $G$. Assume that the closure $\hat{\Phi}$ of $\Phi$ with respect...