Let $X$ be a connected oriented triangulation(polyhedron) space, i.e., homeomorphic to a geometric realization of an oriented simplicial complex $S$ with dimension $n$, and the boundary $\partial S$ of $S$ is 0, is the homology group $H_n(X,Z)$ isomorphic to $Z$?
2026-03-25 16:02:18.1774454538
Homology group of a triangulation(simplicial complex) space
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The answer is no: if $X$ is the wedge of two $n$-spheres, then $H_n(X) \cong \mathbb{Z} \oplus \mathbb{Z}$.