- #1
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Hi, everyone:
I am trying to understand the intersection form, and I am having trouble
with the notation used in Wikipedia's entry on intersection theory:
http://en.wikipedia.org/wiki/Intersection_theory_(mathematics)
Now, I am somewhat weak in my cohomology, and I understand the concept
is necessarily involved, but I would appreciate some comments/insights on
this:
Specifically, in the definition of the bilinear form Qm, on the n-th cohomology
ring H^n(M) :
Qm: H^n(M,delM,Z) x H^n(M, delM; Z)-->Z , given by:
Qm(a,b)=< a\/b, [M] >
where '\/' is the cup product, 'del' is the boundary, and 'Z' are the integers.
Now:
What is this bracket operation < , > ?. It is not stated that M is Riemannian
so I don't see how this would be an inner product. And, what is [M] here ?
I have been reading up in H&Y (Hocking and Young) , and they are using
different notation.
Thanks for Any Help.
I am trying to understand the intersection form, and I am having trouble
with the notation used in Wikipedia's entry on intersection theory:
http://en.wikipedia.org/wiki/Intersection_theory_(mathematics)
Now, I am somewhat weak in my cohomology, and I understand the concept
is necessarily involved, but I would appreciate some comments/insights on
this:
Specifically, in the definition of the bilinear form Qm, on the n-th cohomology
ring H^n(M) :
Qm: H^n(M,delM,Z) x H^n(M, delM; Z)-->Z , given by:
Qm(a,b)=< a\/b, [M] >
where '\/' is the cup product, 'del' is the boundary, and 'Z' are the integers.
Now:
What is this bracket operation < , > ?. It is not stated that M is Riemannian
so I don't see how this would be an inner product. And, what is [M] here ?
I have been reading up in H&Y (Hocking and Young) , and they are using
different notation.
Thanks for Any Help.