Frontiers of Mathematics in China >

2016 , Vol. 11 >Issue 2: 255 - 268

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

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
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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.

Key words： Bott manifold; Bott tower; cohomological rigidity; toric manifold

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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