10
votes
2answers
154 views
+50

Homology Whitehead theorem for non simply connected spaces

(One version of) the Whitehead theorem states that a homology equivalence between simply connected CW complexes is a homotopy equivalence. Does the following generalisation hold true? Suppose ...
0
votes
0answers
18 views

branched cover along a closed curve in the $3$-sphere

Let $c$ be a closed embedded smooth curve in the $3$-sphere $\mathbb S^3$. I was told that $\mathbb S^3$ admits a two fold branched cover $X(c)$, branched along $c$, which corresponds to the ...
2
votes
1answer
158 views

Alternative definition of covering spaces.

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 ...
0
votes
1answer
73 views

Book introducing covering spaces independent of homotopy

Can anyone please suggest a book on algebraic topology which deals with covering spaces independent of homotopy, fundamental group, etc?
1
vote
0answers
34 views

Classification theorem of the coverings of a given space

I'm trying a lot to find easy examples of classification theorems of covering spaces of a given space. I've already read some examples here at Mathexchange such as Classification of covering spaces ...
2
votes
0answers
51 views

Global sections of covering spaces

Let $p:C\to X$ be a covering space having a global section $s:X\to C$. I can show that this implies that $s(X)$ is disconnected from the rest of $C$. Is there any reference where this is explicitly ...
1
vote
0answers
175 views

Completelly cover area with minimum number of maxed circles NP-completeness (or harder) proof

everyone. I'm looking for paper with proof of NP-completeness following, or similar problem. Given: Area $S \subset \mathbb{N}^2$, let it be convex or rectangular, I believe it doesn't matter ...