All Questions
Tagged with branched-covers at.algebraic-topology
7
questions
2
votes
1
answer
80
views
How to determine the LS category of branched covers?
Define the (normalized) Lusternik-Schnirelmann (LS) category of a space $X$, denoted $\mathsf{cat}(X)$ to be the least integer $n$ such that $X$ can be covered by $n+1$ number of open sets $U_i$ each ...
- 21
1
vote
0
answers
107
views
Relation of branched covers and groups
I am self-studying covering spaces of topological spaces. The following question comes to my mind.
In the case of topological covering spaces, we have a nice relation between the fundamental group of ...
- 347
0
votes
1
answer
935
views
What is definition of branched covering?
What is definition of branched covering in the page 10 of following paper ?
In Hatcher, Allen; Lochak, Pierre; Schneps, Leila, On the Teichmüller tower of mapping class groups, J. Reine Angew. Math. ...
- 119
10
votes
1
answer
1k
views
Visualizing genus-two Riemann surfaces: from the three-fold branched cover to the sphere with two handles
I am trying to visualize the genus-two Riemann surface given by the curve
$$
y^3 = \frac{(x-x_1)(x-x_2)}{(x-x_3)(x-x_4)}.
$$
We can regard this surface as a three-fold cover of the sphere with four ...
- 173
4
votes
1
answer
715
views
Monodromy representation of elementary simple covers
Let $X$, $Y$ be smooth, connected, compact manifolds (for instance, projective varieties) and $f \colon X \longrightarrow Y$ be a finite, branched cover of degree $n$, with branch locus $B \subset Y$. ...
- 65.7k
17
votes
3
answers
2k
views
Cohomology of ramified double cover of $\mathbb P^n$ (reference)
Let $X\rightarrow \mathbb P^n_{\mathbb C}$ be a double cover ramified over a smooth hypersurface $B$ of degre $2d$. In the case of hypersurfaces of $\mathbb P^n$ one can determine the integral ...
- 1,443
9
votes
0
answers
334
views
Two transfers for ramified or branched covers
Let $\pi: X \rightarrow Y$ be a 2-fold branched cover of complex varieties. I know of (at least) two types of pushforwards associated to this situation:
If I'm not mistaken, there is a pushforward ...
- 13.3k