 Intersection homology of an even-dimensional suspension

For $\dim L=2n-1$ and lower middle perversity, the suspension with two distinct vertices has $I{H}_i(\mathrm{Susp}L)=I{H}_i(L)$ for $i<n$, zero for $i=n$, and $I{H}_{i-1}(L)$ for $i>n$. Cover it by its two open cones. The Mayer–Vietoris sequence compares their truncated groups with $I{H}_{\ast }(L)$; below $n$ the overlap map is the injective signed diagonal, and above $n$ both cone groups vanish.