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Homotopy theory, homological algebra, algebraic treatments of manifolds.

13 votes
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Low dimensional homotopy groups of $\operatorname{Top}(4)$

$\DeclareMathOperator\Top{Top}$I would like to compute $\pi_3\Top(4)$ and $\pi_4\Top(4)$. It is known that $\Top(4)/O(4) \rightarrow \Top/O$ is 5-connected and $$ \pi_k(\Top/O) = \begin{cases} …
Oleksandr Kharchenko's user avatar