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Homology is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces.

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Generalised homology of a split fibration

For a generalised homology theory $\mathcal{E}_\ast$, there is a splitting $\mathcal{E}_\ast (E)\cong \mathcal{E}_\ast(X)\oplus R_\ast$ induced by $p$ and $s$. …