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Homotopy theory, homological algebra, algebraic treatments of manifolds.
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Euler characteristic of pseudomanifolds with boundary
It is a well-known fact that for every compact oriented odd-dimensional manifold $\mathcal{M}$ with boundary it holds that
$$\chi(\mathcal{M})=\frac{1}{2}\chi(\partial\mathcal{M}).$$
In particular, if …