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Title: Complete square complexes.

Abstract: A "complete square complex" is a 2-complex X whose universal cover is the product of two trees. Obvious examples are when X is itself the product of two graphs but there are many other examples. I will give a quick survey of complete square complexes with an aim towards describing some problems about them and describing some small examples that are "irreducible" in the sense that they do not have a finite cover that is a product.

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