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SimplicialHomology

Guides

  • SimplicialHomology

Symbols

  • BettiNumber
  • HomologyGroup
  • SimplicialAutomorphismGroup
  • SimplicialComplex
  • SimplicialCone
  • SimplicialIsomorphicQ
  • SimplicialJoin
  • SimplicialSuspension
  • SubComplexQ
Taggar`SimplicialHomology`
SimplicialCone
​
SimplicialCone
[sc]
returns the cone of the simplicial complex
sc
.
​
Details and Options
▪
Cone of a simplicial complex
sc
, denoted
C(sc)
is the join of
sc
with a point.
▪
sc
must be a
SimplicialComplex
object.
▪
SimplicialCone
returns a
SimplicialComplex
object.
Examples  
(8)
Basic Examples  
(3)
Find the cone of a simplicial complex:
In[1]:=
SimplicialCone

SimplicialComplex
["Torus"]
Out[1]=
SimplicialComplex
Dimension: 3
Vertices: 8

​
Cone of the
n
-simplex is the
(n+1)
-simplex:
In[1]:=
SimplicialCone

SimplicialComplex
["Point"]
Out[1]=
SimplicialComplex
Dimension: 1
Vertices: 2

​
Taking a cone kills all homology groups:
In[1]:=
HomologyGroup
​​
SimplicialCone

SimplicialComplex
["Torus"],​​"Reduced"True
Out[1]=
00,10,20,30
Properties & Relations  
(5)

SeeAlso
SimplicialComplex
 
▪
SimplicialJoin
RelatedGuides
▪
SimplicialHomology
""

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