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$$\sigma_\mu(A) = -\log\; \mu(A)$$




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August 5th 2023: Added some more navboxes, as if we did not have enough of those yet.

August 4th 2023: Added theorem include box:

include inc:theorem |
title=Poincaré duality|
body=The [[$\mathbb{F}_2$]]-homology of a compact [[$n$]]-dimensional manifold [[$M$]] is symmetric in its grading. That is for all [[$k,n$]], [[$0 \leq k \leq n$]]: [[$$H_k(M; \mathbb{F}_2) \cong H_{n-k}(M; \mathbb{F}_2)$$]]|

will produce:

Poincaré duality

Theorem. The $\mathbb{F}_2$-homology of a compact $n$-dimensional manifold $M$ is symmetric in its grading. That is for all $k,n$, $0 \leq k \leq n$: $$H_k(M; \mathbb{F}_2) \cong H_{n-k}(M; \mathbb{F}_2)$$

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