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Results tagged with lie-groups
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user 104774
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
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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 …
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