Kunneth formula for homology: Difference between revisions
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Suppose <math>X</math> and <math>Y</math> are [[topological space]]s. We then have, for any <math>n \ge 0</math>: | Suppose <math>X</math> and <math>Y</math> are [[topological space]]s. We then have, for any <math>n \ge 0</math>: | ||
<math>H_n(X \times Y) \cong \sum_{i + j = n} H_i(X) \otimes H_j(Y) \oplus \sum_{p + q = n-1} | <math>H_n(X \times Y) \cong \sum_{i + j = n} H_i(X) \otimes H_j(Y) \oplus \sum_{p + q = n-1} Tor(H_p(X),H_q(Y))</math> | ||
==Results used== | ==Results used== | ||
Revision as of 20:17, 3 November 2007
Statement
Suppose and are topological spaces. We then have, for any :
Results used
The Kunneth formula combines the Kunneth theorem and the Eilenberg-Zilber theorem.
Proof
Fill this in later