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Results tagged with at.algebraic-topology
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user 129800
Homotopy theory, homological algebra, algebraic treatments of manifolds.
7
votes
1
answer
479
views
Commutativity up to homotopy implies strict commutativity, for lifting problems
Suppose we have a commutative diagram
$\require{AMScd}$
\begin{CD}
A @>>> X \\
@VVV & @VVV \\
W @>>> Y\\
\end{CD}
where the map $A\rightarrow W$ is a cofibration and the map $X\rightarrow Y$ is …
- 521
5
votes
0
answers
722
views
Questions about obstruction theory (Hatcher's book)
I'm actually studying obstruction theory as presented in the last section of chapter $4$ of the book Algebraic Topology by Allen Hatcher. He first finds condition so that a space $X$ admits a Postnik …
- 521
6
votes
0
answers
208
views
$\mathbb{Z}/2\mathbb{Z}$ coefficients in gysin sequence
I am reading the article "Signature of links" by Kauffman and Taylor. Here they show that it is possible to calculate the nullity of a link $L\subset S^3$ by knowing the first betti number of the doub …
- 521
3
votes
2
answers
399
views
Alexander duality and homology equivalence
While reading the paper of Kauffman and Taylor "Signature of links" I found the following situation.
In the proof of Theorem 2.6 they suppose that two links $L_1, L_2\in \mathbb{S}^3$ are topological …
- 521
3
votes
Alexander duality and homology equivalence
I found a solution for my problem. I post here a brief proof, in case anyone needs it.
I use the version of Alexander Duality, as stated in Bredon's book "Topology and Geometry" that states that if $ …
- 521