Questions tagged [poincare-duality]

For questions involving or related to Poincaré duality.

Poincaré duality is an important result in homology theory, which relates homology and cohomology groups via an isomorphism.

It states that, under appropriate assumptions on a manifold $M$, $$H_{n-k}(M)\cong H^k(M)$$

Consider using this tag along with or one of the associated cohomology tags.

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Poincare Inequality Involving Plancherel

I need help in proving this question: Suppose the function $f$ is differentiable and $\frac{1}{2}$-periodic (i.e., more than just 1-periodic). Show that the Poincare inequality holds with a better constant: $$\int_0^1 f^2(x)dx-\left(\int_0^1…
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