Let $M$ be a smooth (or just topological) closed manifold. Let $C(M)$ denote the cone over $M$, i.e. $C(M)$ equals to $M\times [0,\infty)$ with $M\times \{0\}$ contracted to a point. The image of $M\times \{0\}$ in $C(M)$ is called the origin.

**What is the dualizing complex of $C(M)$? In particular what is its stalk at the origin?**