Künneth theorem

In mathematics, especially in homological algebra and algebraic topology, a Künneth theorem, also called a Künneth formula, is a statement relating the homology of two objects to the homology of their product. The classical statement of the Künneth theorem relates the singular homology of two topological spaces X and Y and their product space ${\displaystyle X\times Y}$. In the simplest possible case the relationship is that of a tensor product, but for applications it is very often necessary to apply certain tools of homological algebra to express the answer.

A Künneth theorem or Künneth formula is true in many different homology and cohomology theories, and the name has become generic. These many results are named for the German mathematician Hermann Künneth.