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Hi, everyone:

I am trying to work with the intersection form in 4-manifolds. Specifically,

I am working with CP^2 $CP^2$ (complex projective 2-space.), whose form is given by <1>.$(1)$.

Now, I know how to compute an actual numerical value when we work with the form in cohomology: we cup-product two cochains a,b , and then evaluate a\/b $a \cup b$ on the fundamental class.

But when we work in homology (using Poincare Duality) , I am not too clear on how we actually get a number by starting with a matrix (we always have representative surfaces for 2-homology in a 4-manifold.). What do we evaluate this matrix in.?

Thanks.

1

# Working with Intersection Forms in Homology. Computation.

Hi, everyone:

I am trying to work with the intersection form in 4-manifolds. Specifically,


I am working with CP^2 (complex projective 2-space.), whose form is given by <1>.

  Now, I know how to compute an actual numerical value when we work with the form


in cohomology: we cup-product two cochains a,b , and then evaluate a\/b on the

fundamental class.

   But when we work in homology (using Poincare Duality) , I am not too clear

on how we actually get a number by starting with a matrix (we always have

representative surfaces for 2-homology in a 4-manifold.). What do we

evaluate this matrix in.?

Thanks.