Cohomolgy "algebras" of compact surfaces
- From: Jeffrey Rolland <jrolland@xxxxxxxxxxxx>
- Date: Tue, 12 Apr 2005 15:09:23 -0500
Hello, all!
I am working on _Characteristic Classes_, which makes copious use of the
cohomology "algebra" (an algebra is a "ring over a field", cohomolgy is
a "ring over a ring") of manifolds, so I am attempting to understand
"algebra" structures as some remedial work. I am working on _Algebraic
Topolgy_ by Greenburg ana Harpur, exercise 24.17, determining the
cohomology "algebras" of the various compact, connected 2-manifolds
without boundary.
In 19.30 and 19.31, the authors give the singular homology of the
surfaces using a CW-complex decomposition with one 2-cell attached to a
rose and a theorem about homology of a space with a single cell
attached. To tackle 24.17, they suggest finding an explict generator of
H_2 and computing the action of the dual of each generator of H_1 on the
generator of H_2.
Any help would be appreciated.
Sincerely,
--
Jeffrey Rolland
<jrolland@xxxxxxxxxxxx>
.
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