Circle as Simplicial Complex

 

sphereSurface:(dim:NNI) -> FiniteSimplicialComplex(VertexSetAbstract) Generate a simplicial complex equivalent to the surface of a hyper-sphere. That is, the surface of a volume with no holes in it, so we use a minimal triangulation of the faces of a single simplex.

 

band:() -> FiniteSimplicialComplex(VertexSetAbstract) Generate a minimal triangulation of the surface of a cylinder without ends

 

Band - Cylinder without ends: (1) -> band() +1 2 3+ |1 2 6| (1) |1 5 6| |2 3 4| |3 4 5| +4 5 6+ Type: FiniteSimplicialComplex(VertexSetAbstract)

Two boundaries, shown in red and blue:

 

EuclideanSpace

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Where Are You

This is one of a series of pages about topology, these pages start here.

For other pages, on the site, about topology see:

• Open Sets
• Fibre bundles
• Simplectical Complexes
• Delta Complexes
• Homotopy
• Homology

Computer Code Implementation

I have written some code to implement algebraic topology structures. This is described on the page here and the actual code is on GitHub here.