cellComplexSphere -- gives a sphere as a cell complex

Synopsis

• Usage:

  cellComplexSphere(R,n)

• Inputs:
  • R, a ring, that specifies the base ring
  • n, an integer, that specifies the dimension of the sphere
• Outputs:
  • a cell complex, an n-dimensional sphere

Description

i1 : S = cellComplexSphere(QQ,3)

o1 = S

o1 : CellComplex

i2 : cells(S)

o2 = HashTable{0 => {Cell of dimension 0 with label 1}}
               3 => {Cell of dimension 3 with label 1}

o2 : HashTable

i3 : chainComplex S

       1       1                   1
o3 = QQ  <-- QQ  <-- 0 <-- 0 <-- QQ
                                  
     -1      0       1     2     3

o3 : ChainComplex

i4 : prune homology S

o4 = -1 : 0  

      0 : 0  

      1 : 0  

      2 : 0  

            1
      3 : QQ

o4 : GradedModule

See also

• cellComplexRPn -- gives a $RP^n$ as a cell complex
• cellComplexTorus -- gives a torus as a cell complex