A $\Delta$ -complex $X$ comes with a filtration by skeleta $X^0 \subseteq \cdots \subseteq X^k \subseteq \cdots \subseteq X$ where the $k$ -skeleton $X^k$ is the union of all images of simplices of dimension at most $k$ .

Example Skeleta of $T^2$ [local-0]

Take the $\Delta$ -complex structure on the torus $T^2$ with one vertex $v$ , three edges $a, b, c$ and two triangles $U, L$ . Slide $k$ to see the $k$ -skeleton, and drag the torus to rotate it.

k = 0

Definition. Skeleta [8CBL]

Example Skeleta of T2T^2T2 [local-0]

Example Skeleta of $T^2$ [local-0]