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?**



Dualizing complex of the cone over a manifold
The stalk of the dualizing complex at a point is the shift of reduced homology of the link at that point. In this case, the link is $M$ and so the homology of the stalk in degree $i$ is $\tilde H\_{i-1}(M)$.


