Manifolds and Cell Complexes
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|Dave Rusin; The Mathematical Atlas|
|A short article designed to provide an introduction to manifolds, spaces like the sphere which look locally like Euclidean space. In particular, these are the spaces in which we can discuss (locally) linear maps, and the spaces in which to discuss smoothness. They include familiar surfaces. Cell complexes are spaces made of pieces which are part of Euclidean space, generalizing polyhedra. These types of spaces admit very precise answers to questions about existence of maps and embeddings; they are particularly amenable to calculations in algebraic topology; they allow a careful distinction of various notions of equivalence. These are the most classic spaces on which groups of transformations act. This is also the setting for knot theory. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus.|
|Math Topics:||Manifolds/Cell Complexes|
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