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Results tagged with at.algebraic-topology
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user 80559
Homotopy theory, homological algebra, algebraic treatments of manifolds.
5
votes
2
answers
589
views
Are there non-contractible spaces $A$ and $B$ such that $A \wedge B$ is contractible?
The question is in the title : Can we find spaces $A$ and $B$, each non contractible, such that their smash product $A \wedge B$, i.e. the homotopy cofibre of $A \vee B \to A \times B$, is a contracti …
- 5,544
8
votes
Are there non-contractible spaces $A$ and $B$ such that $A \wedge B$ is contractible?
Oh yes ! Fernando gave the hint !
Take $A = S^1$ and $B$ = the Epstein's space.
Then $A \wedge B \simeq \Sigma B$ is contractible but $B$ is not !
- 301
6
votes
1
answer
347
views
Can the standard map $\Sigma \Omega X \to X$ be a homotopy equivalence?
The question is in the title : are there spaces X such that the adjoint of the identity on the loop space $\Omega X$, i.e. $\Sigma\Omega X \to X$, is a homotopy equivalence ?
- 18.2k