Cohomological rigidity for Fano Bott manifolds

被引：2

作者：

Higashitani, Akihiro ^{[1
]}

Kurimoto, Kazuki ^{[2
]}

机构：

[1] Osaka Univ, Grad Sch Informat Sci & Technol, Dept Pure & Appl Math, Suita, Osaka 5650871, Japan

[2] Kyoto Sangyo Univ, Grad Sch Sci, Dept Math, Kyoto 6038555, Japan

来源：

MATHEMATISCHE ZEITSCHRIFT | 2022年 / 301卷 / 03期

关键词：

Cohomological rigidity; Toric Fano manifold; Bott manifold; CLASSIFICATION;

D O I：

10.1007/s00209-022-02994-w

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present paper, we characterize Fano Bott manifolds up to diffeomorphism in terms of three operations on matrix. More precisely, we prove that given two Fano Bott manifolds X and X', the following conditions are equivalent: (1) the upper triangular matrix associated to X can be transformed into that of X' by those three operations; (2) X and X' are diffeomorphic; (3) the integral cohomology rings of X and X' are isomorphic as graded rings. As a consequence, we affirmatively answer the cohomological rigidity problem for Fano Bott manifolds.

引用

页码：2369 / 2391

页数：23

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