Classification of Bott towers by matrix

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A criterion for the classification of Bott towers is presented, i.e., two Bott towers B*(A) and B*(A′) are isomorphic if and only if the matrices A and A′ are equivalent. The equivalence relation is defined by two operations on matrices. And it is based on the observation that any Bott tower B*(A) is uniquely determined by its structure matrix A, which is a strictly upper triangular integer matrix. The classification of Bott towers is closely related to the cohomological rigidity problem for both Bott towers and Bott manifolds.