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{wiki=Gysin_sequence}

For the unit sphere bundle $S(E)\to B$ of an oriented rank-$d$ vector bundle, the Gysin sequence contains
$$
\cdots\to H^{q-d}(B)\xrightarrow{\smile e(E)}H^q(B)\to H^q(S(E))\to H^{q-d+1}(B)\xrightarrow{\smile e(E)}H^{q+1}(B)\to\cdots.
$$


Gysin sequence of a sphere bundle

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 114 / 3 / d / Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 114 / 3 / Solution

Gysin sequence of a sphere bundle

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Gysin sequence of a sphere bundle

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