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 t...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.展开更多
基金This work was supported in part by the National Natural Science Foundation of China （Grant No. 11201170）.
文摘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.
