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Results tagged with at.algebraic-topology
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user 59302
Homotopy theory, homological algebra, algebraic treatments of manifolds.
21
votes
Rational homotopy groups of $S^2\vee S^2$
Piotr, I think the question you really want to ask is:
Given a map $f:S^n \to S^2 \vee S^2$, how do I prove that it is homotopically nontrivial?
This is the so-called homotopy period problem, and it …
- 934
7
votes
Accepted
A homeomorphism with a prescribed action on the fundamental group - decidable or not?
This is undecidable. For a construction, see the first page of Nabutovsky and Weinberger, "Algorithmic aspects of homeomorphism problems", Rothenberg Festschrift 1998.
- 934
14
votes
1
answer
1k
views
Whitehead products in homotopy groups of spheres
Here is what I know about Whitehead products in homotopy groups of spheres:
$[\mathrm{id}_{S^{2n}},\mathrm{id}_{S^{2n}}]$ has Hopf invariant (EDIT: $\pm$) two.
No element that survives into the stab …
- 934
3
votes
A variant of $\ell^2$-cochains
I'm not sure if this should be a comment rather than an answer, since I'm not attempting to answer the hard questions (2) and (3). But it's too long to be a comment. That said:
First of all, I just …
- 934