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SimplicialHomology

Guides

  • SimplicialHomology

Symbols

  • BettiNumber
  • HomologyGroup
  • SimplicialAutomorphismGroup
  • SimplicialComplex
  • SimplicialCone
  • SimplicialIsomorphicQ
  • SimplicialJoin
  • SimplicialSuspension
  • SubComplexQ
Taggar`SimplicialHomology`
SimplicialSuspension
​
SimplicialSuspension
[sc]
returns the suspension of the simplicial complex
sc
.
​
Details and Options
▪
Suspension of a simplicial complex
sc
, denoted
S(sc)
is the join of
sc
with a point.
▪
sc
must be a
SimplicialComplex
object.
▪
SimplicialSuspension
returns a
SimplicialComplex
object.
Examples  
(7)
Basic Examples  
(3)
Find the suspension of a simplicial complex:
In[1]:=
SimplicialSuspension

SimplicialComplex
["Torus"]
Out[1]=
SimplicialComplex
Dimension: 3
Vertices: 9

​
Cone of the 2-simplex is two tetrahedra glued along the common face:
In[1]:=
SimplicialSuspension

SimplicialComplex
["Triangle"]
Out[1]=
SimplicialComplex
Dimension: 3
Vertices: 5

In[2]:=
%["1Skeleton"]
Out[2]=
​
Suspension of
SimplicialComplex
[{"Circle",n}]
is
SimplicialComplex
[{"Circle",n+1}]
:
In[1]:=
HomologyGroup
sn=
SimplicialComplex
[{"Circle",2}]
Out[1]=
0,10,2
In[2]:=
HomologyGroup

SimplicialSuspension
[sn]
Out[2]=
0,10,20,3
Properties & Relations  
(4)

SeeAlso
SimplicialComplex
 
▪
SimplicialJoin
RelatedGuides
▪
SimplicialHomology
""

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