# A Sample Computation of Intersection Homology

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

## Abstract

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 :
$$\begin{gathered} {\text{T}}_a^1 {\text{ = S}}^{\text{1}} \times {\text{\{ p\} }} \times {\text{\{ p\} ; T}}_b^1 {\text{ = \{ p\} }} \times {\text{S}}^{\text{1}} \times {\text{\{ p\} ;T}}_c^1 {\text{ = \{ p\} }} \times {\text{\{ p\} }} \times {\text{S}}^{\text{1}} \hfill \\ {\text{T}}_a^2 {\text{ = \{ p\} }} \times {\text{S}}^{\text{1}} \times {\text{S}}^{\text{1}} {\text{; T}}_b^2 = {\text{S}}^{\text{1}} \times {\text{\{ p\} }} \times {\text{S}}^{\text{1}} ;{\text{T}}_c^2 {\text{ = S}}^{\text{1}} \times {\text{S}}^{\text{1}} \times {\text{\{ p\} }}{\text{.}} \hfill \\ \end{gathered}$$

## Keywords

Betti Number Algebraic Topology Single Number Sample Computation Local Homology
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