# Alexander-Whiteney duality

## Main Question or Discussion Point

What is Alexander-Whitney duality?

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It's not a common term, but I assume you are really referring to the Alexander-Whitney map.

If $$X$$, $$Y$$ are topological spaces, then the AW map is the natural transformation between:

$$(X, Y) \mapsto Sing (X \times Y)$$ and $$Sing (X) \otimes Sing (Y)$$

Where $$Sing$$ is total singular chain complex for the specified top. space.

Since it's a http://en.wikipedia.org/wiki/Natural_transformation" [Broken], it could be labeled a duality.

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Hurkyl
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