Frontiers of Mathematics in China >
Classification of Bott towers by matrix
Received date: 18 Mar 2014
Accepted date: 23 Sep 2015
Published date: 18 Apr 2016
Copyright
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
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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