On 02/07/16 21:15, Waldek Hebisch wrote:
If you slightly generalize notion of simplicial complex to allow simplices with equal vertices, then you may use just one node and n copies of 1 dimensional simplex [0 0]. Of course the fundamental group is free group on n generators.
Do you think it would be reasonable to allow this in DeltaComplex but not in FiniteSimplicialComplex or FiniteCubicalComplex?
As usual I guess we have to clarify definitions. Hatcher (p102) gives delta complexes as a "mild generalization of the more classical notion of a simplical complex".
I get the impression that this "mild generalization" is allowing multiple copies of facets? For instance, instead of the minimal triangulation of a projective plane having 10 triangles it can be represented as a square (2 triangles) where the opposite edges are the same (but with opposite orientation).
The other difference in the code between delta and simplicial complexes is that in simplicial complexes everything is defined (indexed) directly in terms of vertices but in DeltaComplex indexing is in terms of next lower dimension (differential form???).
I had not tested this, even for DeltaComplex, but your tests look promising. It would be good to pursue this.
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