Are there good references reporting the computation of homology of (non necessarily convex) open cones of $\mathbb{R}^n$ ? Here by cone we mean subset of $\mathbb{R}^n$ invariant by the natural action of $\mathbb{R}^*$.
The idea behind is to get a good intuition of it in order to compute the dual of the cohomology of the cone in the following sense :
let $k$ be a commutative field, for an open cone $\gamma$, let us denote by $\overline{\gamma}$ its adherence, $k_{\overline{\gamma}}$ the sheaf constant with stalks $\mathbb{R}$ on $\gamma$ and $R\mathrm{hom}$ the derived functor of the $hom$ bifunctor.
I want to compute the derived "dual" $R\mathrm{hom}(k_{\overline{\gamma}},k_{\mathbb{R}^n})$.