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Let $\Omega$ be a regular, finite, $n$-dimensional CW complex with chain modules $\mathscr{C}_k$ and boundary operators $\partial_k$. For many problems in computational geometry, a key operation is to ...

(I have asked this question at math stackexchange, it was upvoted but got no answers; maybe you can help.) It is well-known that $\beta_1(R(f))\le\beta_1(X)$, where $\beta_1$ is the first Betti ...