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SimplicialHomology

Guides

  • SimplicialHomology

Symbols

  • BettiNumber
  • HomologyGroup
  • SimplicialAutomorphismGroup
  • SimplicialComplex
  • SimplicialCone
  • SimplicialIsomorphicQ
  • SimplicialJoin
  • SimplicialSuspension
  • SubComplexQ
Taggar`SimplicialHomology`
SimplicialJoin
​
SimplicialJoin
[
SimplicialComplex
[…],
SimplicialComplex
[…],…]
constructs the join product of given simplicial complexes.
​
Details and Options
▪
The simplicial join is formed by taking pairwise union of all simplices of the given complexes.
▪
SimplicialJoin
relabels the vertex sets.
▪
The join of simplicial complexes
sc
1
and
sc
2
is denoted by
sc
1
*
sc
2
, and so on.
Examples  
(6)
Basic Examples  
(2)
Joining two points results in a line:
In[1]:=
SimplicialJoin

SimplicialComplex
[{{1}}],
SimplicialComplex
[{{2}}]
Out[1]=
SimplicialComplex
Dimension: 1
Vertices: 2

​
Joining a line with a point results in a triangle (2-simplex):
In[1]:=
SimplicialJoin

SimplicialComplex
[{{1}}],
SimplicialComplex
[{{2,3}}]
Out[1]=
SimplicialComplex
Dimension: 2
Vertices: 3

Properties & Relations  
(4)

SeeAlso
SimplicialComplex
RelatedGuides
▪
SimplicialHomology
""

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