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arXiv · 2008.05811

Cohomological rigidity for Fano Bott manifolds

Akihiro Higashitani·Kazuki Kurimoto
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Abstract

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.

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Akihiro Higashitani, Kazuki Kurimoto. 2020-08-13. Cohomological rigidity for Fano Bott manifolds. https://arxiv.org/abs/2008.05811

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