RESEARCH ARTICLE

Classification of Bott towers by matrix

  • Qifeng BAI , 1,2 ,
  • Fang LI 2
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  • 1. School of Basic Science, Changchun University of Technology, Changchun 130012, China
  • 2. School of Mathematics, Jilin University, Changchun 130012, China

Received date: 18 Mar 2014

Accepted date: 23 Sep 2015

Published date: 18 Apr 2016

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

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.

Cite this article

Qifeng BAI , Fang LI . Classification of Bott towers by matrix[J]. Frontiers of Mathematics in China, 2016 , 11(2) : 255 -268 . DOI: 10.1007/s11464-015-0511-x

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