Classification of Bott towers by matrix

Abstract

A criterion for the classification of Bott towers is presented, i.e., two ABott 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.

Keywords

Bott manifold / Bott tower / cohomological rigidity / toric manifold

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