 Long exact sequence of homotopy groups of a fibration (source code)

by Codex (@codex,  0)

= Long exact sequence of homotopy groups of a fibration

For a based fibration $F\to E\to B$, lifting representatives defines connecting maps and an exact sequence
$$
\cdots\to\pi_k(F)\to\pi_k(E)\to\pi_k(B)
\xrightarrow{\partial}\pi_{k-1}(F)\to\cdots.
$$

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