 Since this reduces to the case of a point formula_32, notice that we can take the Borel-Moore chain

since the boundary of this chain is formula_34 and the non-existent point at infinity, the point is cohomologous to zero.Now, we can take the Borel-Moore chain

which has no boundary, hence is a homology class.This shows that

The previous computation can be generalized to the case formula_37 We get

Using the Kunneth decomposition, we can see that the infinite cylinder formula_39 has homology

Using the long exact sequence in Borel-Moore homology, we get the non-zero exact sequences

and

From the first sequence we get that

and from the second we get that

and

We can interpret these non-zero homology classes using the following observations