All Questions

Let $X$ and $Y$ be topological manifolds and let $\{(\phi_x,U_x)\}_{x \in X}$ and $\{(\psi_y,Y_y)\}_{y \in Y}$ be respective atlases of $X$ and $Y$; with each $\phi_x:U_x\rightarrow \mathbb{R}^n,\...

I'm going through the crisis of being unhappy with the textbook definition of a differentiable manifold. I'm wondering whether there is a sheaf-theoretic approach which will make me happier. In a ...

Let $X$ be a complex manifold, $F$ a bounded complex of $\Bbb C_X$-modules with constructible cohomology. If the set $\{x: F_x\neq0\}$ is relatively open (i.e. open in its closure), is the same true ...

I fairly understand the fiber bundles, both the mathematical concept of fiber bundles and the physics use of fiber bundles. Because the fiber bundles are tightly connected to the gauge field theory in ...