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Results tagged with at.algebraic-topology
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user 104774
Homotopy theory, homological algebra, algebraic treatments of manifolds.
3
votes
1
answer
337
views
Homotopy type of $SO(4)/SO(2)$
A classical result states that the quotient $SO(4)/SO(3)$ is homotopy equivalent to $S^3$. In fact, this can be stated in more general terms since $SO(n+1)/SO(n)$ has the homotopy type of $S^n$. What …
- 325
8
votes
2
answers
421
views
Relationship between induced maps at homotopy groups level for maps $f:S^2\to S^2$
It is a known result that based point maps $f:S^2\to S^2$ are classified by their degree. That is, by the induced map at $\pi_2$-level $f_{*2}:\pi_2(S^2)\to\pi_2(S^2)$ (the subindex $*2$ just means it …
- 325