Talk:Simplicial complex

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Mathematics rating:	Start Class	Mid Priority	Field: Topology
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Geometry guy 23:40, 20 May 2007 (UTC)

[edit] Merge simplicial complex & abstract simplicial complex?

It may eliminate some redundancy (and confusion) if simplicial complex and abstract simplicial complex are put on the same page -- especially since the difference between the two is fairly minor.

Trevorgoodchild 03:31, 1 February 2007 (UTC)

Disagreed. "Some" redundancy does not hurt. What kind of confusion you are talking about? `'mikka 23:05, 1 February 2007 (UTC)

I guess I don't know why we need simplicial complex:geometry AND simplicial complex:algebraic topology AND abstract simplicial complex as three separate things, each with its own independent definition. The differences among the three are extremely superficial. Trevorgoodchild 15:44, 2 February 2007 (UTC)

Not at all superficial. To a pure algebraic topologist it may appear so (I am guessing here), but to a student of partially ordered sets the difference between an abstract simplicial complex and any other kind is important; the questions and examples are different. To a geometer the difference between a truly geometrical realization and an abstract or topological complex is important, for instance, the geometrical realization of a simplex may be a rigid body like a convex polytope. It is nonetheless true that there are very close relationships and for some purposes the concepts are not significantly different. Zaslav 11:34, 20 March 2007 (UTC)

[edit] what is not a simplicial complex

I believe that it should be emphasized that the intersection of two faces must be a SINGLE simplex. e.g.,, two edges cannot form a cycle. This has caused me some confusion in the past. —The preceding unsigned comment was added by 169.233.53.82 (talk) 21:11, 15 April 2007 (UTC).

[edit] Relationship to a Manifold

A manifold has fixed dimension; obviously a simplicial complex does not. Is there a generalization of a simplicial complex that is more "manifold-like". For example, the set { a circular disk, a point, a line segment connected to the surface of an ellipsoid } is homeomorphic to the set { a triangle, a point, a line segment connected to the vertex of a tetrahedron }. What would you call that first set? —Ben FrantzDale 16:34, 6 May 2007 (UTC)

It looks like the answer is "a CW complex". Is that right? —Ben FrantzDale 18:57, 6 May 2007 (UTC)