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Classification of Bott towers by matrix

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Abstract

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.

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Authors and Affiliations

  1. School of Basic Science, Changchun University of Technology, Changchun, 130012, China

    Qifeng Bai

  2. School of Mathematics, Jilin University, Changchun, 130012, China

    Qifeng Bai & Fang Li

Authors
  1. Qifeng Bai
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  2. Fang Li
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Correspondence to Qifeng Bai.

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Bai, Q., Li, F. Classification of Bott towers by matrix. Front. Math. China 11, 255–268 (2016). https://doi.org/10.1007/s11464-015-0511-x

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  • DOI: https://doi.org/10.1007/s11464-015-0511-x

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