n-skeleton

Summary

The $n$-skeleton of a CW complex or of a simplicial complex is the part made of the cells or simplices of dimension at most $n$. The skeleta form an increasing sequence of subcomplexes whose union is the whole complex. Each one is built from the previous one by attaching $n$-dimensional cells. Induction over the skeleta is the main technique for proving facts about CW complexes. The $n$-skeleton already determines the homotopy groups of the complex below degree $n$.