I have a question about covering maps. If $\phi_1: X_1 \rightarrow Y_1$ is a covering map, and $\phi_2: X_2 \rightarrow Y_2$ is a covering map, then is it true that $\phi_1 \times \phi_2: X_1 \times X_2 \rightarrow Y_1 \times Y_2$ a covering map?

Suppose $M$ is a manifold, topological or smooth etc. As a topological space $M$ is required to be primarily locally homeomorphic to $\Bbb R^n$, with some added things that don’t come along with this, like a global Hausdorff condition mentioned here, second countability or paracompactness etc. Mainly it would seem to rule out certain pathological […]

I need to describe how a 4-genus orientable surface double covers a genus 5-non-orientable surface. I know that in general every non-orientable compact surface of genus $n\geq 1$ has a two sheeted covering by an orientable one of genus n-1. I tried to use the polygonal representation of these surfaces and try to get one […]

I am trying to understand in more detail the answer to: Universal Cover of a Surface (with Boundary) It is mentioned that the universal cover of a hyperbolic surface $S$ with geodesic boundary is a closed disk $D^2$ with a Cantor set removed from its boundary. I am trying to see what the preimage of […]

I would like to construct a covering space of a wedge of two circles with a given normal subgroup $H \subset \pi_{1}(S^{1} \vee S^{1})=F_{a,b}$. The goal is to find a covering space $\tilde{X}$ so that $p_{*}(\pi_{1}{(\tilde{X}}))=H$, where $p: \tilde{X} \rightarrow X$. First, for more or less non-sophisticated cases it’s not very diffucult to notice, how […]

in a lecture I have seen a definition of a covering space, different from what I would call the usual one (e.g. the one in Munkres): A surjective continuous map $p:E\rightarrow B$ of spaces $E$ and $B$ is a covering map (and $E$ a covering space of $B$) if for every $b\in B$ there is […]

I am stuck on the following exercise: Let $Y$ be a compact topological space, and $p:\ Y\ \longrightarrow\ X$ a covering map. Show that for every $x\in X$ the fibre $p^{-1}(x)$ is finite. Any help would be very welcome.

Let $(M,g)$ be a connected Riemannian manifold which admits a universal cover $(\tilde{M}, \tilde{g})$, where $\tilde{g}$ is the Riemannian metric such that the covering is a Riemannian covering. I want to know under what conditions the universal cover $\tilde{M}$ is complete. The reason for this questions is that I want to know under what conditions […]

I wish to prove the following statement: Let $X$ be a simply connected and locally connected space, and let $p:Y\to Z$ be a covering map. Then given $f:X\to Z$ continuous, $x_0\in X$, $y_0\in Y$ such that $p(y_0)=f(x_0)$, there is a unique continuous function (a “lift”) $\tilde f:X\to Y$ such that $p\circ\tilde f=f$ and $\tilde f(x_0)=y_0$. […]

My question involves topological spaces $X$, $Y$ and $Z$, two coverings $p : Y \rightarrow X$ and $q: Z \rightarrow X$ of $X$ and a morphism $f: Y \rightarrow Z$ of coverings, i.e. a map which fulfills $p = q \circ f$. My question is: Is $f$ itself a covering map $Y \rightarrow Z$ ? […]

Intereting Posts

What is the combinatoric significance of an integral related to the exponential generating function?
Show that $f(x+y)=f(x)+f(y)$ implies $f$ continuous $\Leftrightarrow$ $f$ measurable
$\sum_{n=1}^{\infty}(-1)^{n-1}\left({\beta(n)\over n}-\ln{n+1\over n}\right)=\ln\sqrt{2\over \pi}\cdot{2\over \Gamma^2\left({3\over 4}\right)}?$
Evaluate the improper integral $ \int_0^1 \frac{\ln(1+x)}{x}\,dx $
Property of Entire Functions
How to integrate $\int x\sin {(\sqrt{x})}\, dx$
A query about Poisson summation and matrices
Determining whether the series $\sum_{n=1}^{\infty} \frac{\sqrt{n}+\sin(n)}{n^2+5}$ is convergent or divergent by comparison test
Errors of Euler interpretation?
What are large cardinals for?
Degree of the difference of two roots
Prove that the only sets in $R$ which are both open and closed are the empty set and $R$ itself.
Help with a limit of an integral: $\lim_{h\to \infty}h\int_{0}^\infty{{ {e}^{-hx}f(x)} dx}=f(0)$
How many solutions are there to $x_1 + x_2 + … + x_5 = 21$?
Is the ideal generated by an irreducible polynomial prime?