cup product
Let be a topological space and be a commutative ring. The diagonal map induces a chain map between singular cochain complexes:
.
Let
denote the chain homotopy equivalence associated with the Kunneth .
Given and we define
.
As and are chain maps, induces a well defined product on cohomology groups, known as the cup product. Hence the direct sum of the cohomology groups of has the structure of a ring. This is called the cohomology ring of .
Title | cup product |
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Canonical name | CupProduct |
Date of creation | 2013-03-22 15:37:42 |
Last modified on | 2013-03-22 15:37:42 |
Owner | whm22 (2009) |
Last modified by | whm22 (2009) |
Numerical id | 7 |
Author | whm22 (2009) |
Entry type | Definition |
Classification | msc 55N45 |