Let $M$ be the oriented $m$-manifold. Futhermore, $M$ is not closed. Then how we show that $\beta_{m-1}(M-\{P_{1},\ldots,P_{n}\})=\beta_{m-1}(M)+n,$ where $M-\{P_{1},\ldots,P_{n}\}$ is n-times punctured manifold.
2026-02-23 02:12:27.1771812747
A non-vanishing Betti number of punctured manifolds
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