I am interested in the barycentric subdivision of closed homology manifolds.


**Definition** A (finite) simplicial complex $K$ is a *closed homology manifold* of dimension $n$ if for every $k$-simplex, its link has the homology of $\mathbb{S}^{n-k-1}$.


I wonder whether the barycentric subdivision of a closed homology manifold remains a closed homology manifold and if case it does not, if there are some extra (minimal) conditions I can add to guarantee that.


Do you know of a reference where this or related questions are addressed?


(I have not found an answer in Rourke and Sanderson's "Introduction to Piecewise linear topology", which was my first try.)


Thanks in advance for your time



Subdivision of closed homology manifold reference request
Using excision, and the decomposition of the star of a simplex $\sigma$ as $\sigma \* \mathrm{Lk}(\sigma)$, you can easily show that your definition is equivalent to asking that
$$H\_i(|K|, |K| \setminus \{x\} ;\mathbb{Z}) = \begin{cases}\mathbb{Z} & \text{ if $i=n$}\\
0 & \text{ else}.\end{cases}, \text{ for every $x \in |K|$}.$$
But this (re)definition of homology manifold only depends on the topological space $|K|$, which is unchanged under barycentric subdivision.


