Skeleton

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• Cell complex

The k-skeleton of a cubical complex K (or any cell complex) is the complex $K^{(k)}$ consisting of all of $i$-cells of $K$ with $i≤k$.

Example. This is complex $K$:

Below are the $0$-, $1$-, and $2$-skeletons of $K$.

$0$-skeleton:

$1$-skeleton:

$2$-skeleton:

Higher dimensional skeleta of $K$ still make sense but they are all identical to the last one.

Note: To compute the $k$-homology of a complex it suffices to know its $(k+1)$-skeleton.

Example. A cell complex's skeleta: