All Questions

Let $X$ be a finite CW complex. Swan's theorem provide an equivalence $$ {\rm Vec}(X)\xrightarrow\sim{\rm ProjMod}(\mathop{\rm hom}\nolimits_{\rm Top}(X,\mathbb{R})) $$ between the category of finite ...

I just read about the definitions about torsor of sheaf of groups and get a bit confused. How does the notion of $G$-torsor for a topological space compared to that of a sheaf of groups? Is there a ...

Given a vector bundle $E \to M$ with connection $\nabla$, we get a twisted de Rham sequence using the exterior covariant derivative: $$\mathcal{E} \xrightarrow{d^\nabla=\nabla} \Omega^1_M \otimes_{\...