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SimplicialHomology

Guides

  • SimplicialHomology

Symbols

  • BettiNumber
  • HomologyGroup
  • SimplicialAutomorphismGroup
  • SimplicialComplex
  • SimplicialCone
  • SimplicialIsomorphicQ
  • SimplicialJoin
  • SimplicialLink
  • SimplicialProduct
  • SimplicialStar
  • SimplicialSuspension
  • SubComplexQ
Taggar`SimplicialHomology`
SimplicialLink
​
SimplicialLink
[sc,sigma]
returns the link of
sigma
in
sc
.
​
Details and Options
▪
sc
must be a
SimplicialComplex
and
sigma
must be a simplex in
sc
.
▪
Link of
sigma
is the complex formed by all simplices that are disjoint from
sigma
and whose union with
sigma
is a simplex of the complex.
Examples  
(4)
Basic Examples  
(3)
Link of a point of given square:
In[1]:=
SimplicialLink
​​
SimplicialComplex
[{{1,2},{2,3},{3,4},{1,4}}],​​{1}​​
Out[1]=
SimplicialComplex
Dimension: 0
Vertices: 2

​
Link of an interior vertex in a 2-Manifold:
In[1]:=
SimplicialLink
​​
SimplicialComplex
[{{1,2,3},{1,3,4},{1,4,5},{1,5,6},{1,6,7},{1,7,2}}],​​{1}​​
Out[1]=
SimplicialComplex
Dimension: 1
Vertices: 6

​
In[1]:=
sc=
SimplicialComplex
[{{1,2,3},{2,3,4}}]
Out[1]=
SimplicialComplex
Dimension: 2
Vertices: 4

Link of various simplices:
In[2]:=
SimplicialLink
[sc,{1}]
Out[2]=
SimplicialComplex
Dimension: 1
Vertices: 2

In[3]:=
SimplicialLink
[sc,{2}]
Out[3]=
SimplicialComplex
Dimension: 1
Vertices: 3

In[4]:=
SimplicialLink
[sc,{2,3}]
Out[4]=
SimplicialComplex
Dimension: 0
Vertices: 2

Properties & Relations  
(1)

SeeAlso
SimplicialComplex
 
▪
SimplicialStar
""

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