In "Théorie des Faisceaux", Godement states the following theorem due to Leray (Theorem 5.2.5, page 209). Let ${\mathcal M}=(M_i )_{i\in I}$ be a locally finite closed covering o …

I'm looking for the answer to following question. Do exist different knots in $RP^3$ which have equivalent liftings in $S^3$ under covering $p:S^3\rightarrow RP^3$?

I have the following questiom: let $X$ and $Y$ be two different points (represented by Riemann surfaces) in the Teichmuller space $T_g$ of genus $g \geq 2$ Riemann surfaces. Then o …

For a presheaf $F$ on a category equipped with a pretopology, one has the sheafification $F^{\sharp}$ of $F$. I know well the plus-construction of sheafification, which is present …

Let $X$ and $Y$ be locally comapct Hausdorff spaces, and $f:X\to Y$ be a surjective local homeomorphism. When is $f$ a covering map? It is well-known that when $f$ is proper, $f$ …

(where c>0 and the balls need not be disjoint?) This is an embarrassingly simple question, yet somehow I couldn't find an answer (not even, "this is a well-known open problem") …

This is an improved and hopefully a more precise version of the question http://mathoverflow.net/questions/104718/covering-spaces-of-surfaces. Question: Given a regular covering m …

Cyclic coverings of $\mathbb{P^{1}}$ have a simple (affine) equation, namely the formula, $y^{m}= (x_{1}-a_{1})^{t_{1}}....(x_{n}-a_{n})^{t_{n}}$. Is there such a nice equation for …

If $\pi: C \rightarrow \mathbb{P}^{1}$ is a cyclic cover of $\mathbb{P}^{1}$ with Galois group $\mathbb{Z}/m \mathbb{Z}$ and thus with the (affine) formula $y^{m}= (x_{1}-a_{1})^{ …