Editing CW complex (section)

=== Finite-dimensional CW complexes ===
Some examples of finite-dimensional CW complexes are:<ref name=":1" />
* '''An [[n-sphere|''n''-dimensional sphere]]'''. It admits a CW structure with two cells, one 0-cell and one n-cell. Here the n-cell <math>D^{n}</math> is attached by the constant mapping from its boundary <math>S^{n-1}</math> to the single 0-cell. An alternative cell decomposition has one (''n''-1)-dimensional sphere (the "[[equator]]") and two ''n''-cells that are attached to it (the "upper hemi-sphere" and the "lower hemi-sphere").  Inductively, this gives <math>S^n</math> a CW decomposition with two cells in every dimension k such that <math>0 \leq k \leq n</math>.
* '''The ''n''-dimensional real [[projective space]].''' It admits a CW structure with one cell in each dimension.
* The terminology for a generic 2-dimensional CW complex is a '''shadow'''.<ref>{{cite book |last=Turaev |first=V. G. |title=Quantum invariants of knots and 3-manifolds |date=1994 |publisher=Walter de Gruyter & Co. |isbn=9783110435221 |series=De Gruyter Studies in Mathematics |volume=18 |location=Berlin}}</ref>
* A [[polyhedron]] is naturally a CW complex.
*[[Grassmannian]] manifolds admit a CW structure called '''Schubert cells'''.
*[[Differentiable manifold]]s, algebraic and projective [[algebraic variety|varieties]] have the [[homotopy type]] of CW complexes.
* The [[Alexandroff extension|one-point compactification]] of a cusped [[hyperbolic manifold]] has a canonical CW decomposition with only one 0-cell (the compactification point) called the '''Epstein–Penner Decomposition'''. Such cell decompositions are frequently called '''ideal polyhedral decompositions''' and are used in popular computer software, such as [[SnapPea]].