A Sample Computation of Intersection Homology

  • M. Goresky
  • R. MacPherson
Part of the Modern Birkhäuser Classics book series (MBC, volume 50)


In this example we compute the intersection homology of the Cartesian product of S1 with the suspension of the 3-torus. We use the notation X = (ΣT3) × S1. By choosing a basepoint {p} in S1 we can identify the following cycles in T3 :
$$ \begin{gathered} {\text{T}}_a^1 {\text{ = S}}^{\text{1}} \times {\text{\{ p\} }} \times {\text{\{ p\} ; T}}_b^1 {\text{ = \{ p\} }} \times {\text{S}}^{\text{1}} \times {\text{\{ p\} ;T}}_c^1 {\text{ = \{ p\} }} \times {\text{\{ p\} }} \times {\text{S}}^{\text{1}} \hfill \\ {\text{T}}_a^2 {\text{ = \{ p\} }} \times {\text{S}}^{\text{1}} \times {\text{S}}^{\text{1}} {\text{; T}}_b^2 = {\text{S}}^{\text{1}} \times {\text{\{ p\} }} \times {\text{S}}^{\text{1}} ;{\text{T}}_c^2 {\text{ = S}}^{\text{1}} \times {\text{S}}^{\text{1}} \times {\text{\{ p\} }}{\text{.}} \hfill \\ \end{gathered} $$


Betti Number Algebraic Topology Single Number Sample Computation Local Homology 


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Copyright information

© Birkhäuser Boston, Inc. 1984

Authors and Affiliations

  • M. Goresky
    • 1
  • R. MacPherson
    • 2
  1. 1.Department of MathematicsNortheastern UniversityBostonUSA
  2. 2.Department of MathematicsBrown UniversityProvidenceUSA

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