= Intersection cohomology
{title2=$IH_{\bar p}^i(X)$}
In the Deligne-sheaf convention, $IH_{\bar p}^i(X)=\mathbb H^i(X,IC_{\bar p})$, with $IC_{\bar p}$ normalized in degree zero on the regular stratum. For a compact oriented $N$-dimensional pseudomanifold over a field, $IH_{\bar p}^i(X)\cong IH_{N-i}^{\bar p}(X)$ and it is dual to $IH_i^{\bar q}(X)$, where $\bar p(k)+\bar q(k)=k-2$. Thus the dual of lower-middle <singular chains> uses the upper-middle Deligne <sheaf>. The two middle conventions agree on <Witt spaces>.
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