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reduced cohomology

For a cohomology theory $E$ with cohomology groups $E(X)$ the reduced cohomology of $E$ for pointed topological spaces $X$ is on $X$ the kernel

$$E_{\mathrm{red}}(X):=\ker (E(*\to X):E(X)\to E(*))$$E_{red}(X) := ker\left(E({*} \to X) : E(X) \to E(*)\right)

of the map $E(X)\to E(*)$ induced from the point inclusion $*\to X$.

related entries

See

• A Survey of Elliptic Cohomology - cohomology theories

for a bit of context.