### Abstract

A Bott manifold is the total space of some iterated ℂℙ^{1} –bundles over a point. We prove that any graded ring isomorphism between the cohomology rings of two Bott manifolds preserves their Pontrjagin classes. Moreover, we prove that such an isomorphism is induced from a diffeomorphism if the Bott manifolds are ℤ/2– trivial, where a Bott manifold is called ℤ/2–trivial if its cohomology ring with ℤ/2–coefficients is isomorphic to that of a product of copies of ℂℙ^{1}.

Original language | English |
---|---|

Pages (from-to) | 965-986 |

Number of pages | 22 |

Journal | Algebraic and Geometric Topology |

Volume | 15 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2015 Apr 22 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Algebraic and Geometric Topology*,

*15*(2), 965-986. https://doi.org/10.2140/agt.2015.15.965

**Invariance of pontrjagin classes for bott manifolds.** / Choi, Suyoung; Masuda, Mikiya; Murai, Satoshi.

Research output: Contribution to journal › Article

*Algebraic and Geometric Topology*, vol. 15, no. 2, pp. 965-986. https://doi.org/10.2140/agt.2015.15.965

}

TY - JOUR

T1 - Invariance of pontrjagin classes for bott manifolds

AU - Choi, Suyoung

AU - Masuda, Mikiya

AU - Murai, Satoshi

PY - 2015/4/22

Y1 - 2015/4/22

N2 - A Bott manifold is the total space of some iterated ℂℙ1 –bundles over a point. We prove that any graded ring isomorphism between the cohomology rings of two Bott manifolds preserves their Pontrjagin classes. Moreover, we prove that such an isomorphism is induced from a diffeomorphism if the Bott manifolds are ℤ/2– trivial, where a Bott manifold is called ℤ/2–trivial if its cohomology ring with ℤ/2–coefficients is isomorphic to that of a product of copies of ℂℙ1.

AB - A Bott manifold is the total space of some iterated ℂℙ1 –bundles over a point. We prove that any graded ring isomorphism between the cohomology rings of two Bott manifolds preserves their Pontrjagin classes. Moreover, we prove that such an isomorphism is induced from a diffeomorphism if the Bott manifolds are ℤ/2– trivial, where a Bott manifold is called ℤ/2–trivial if its cohomology ring with ℤ/2–coefficients is isomorphic to that of a product of copies of ℂℙ1.

UR - http://www.scopus.com/inward/record.url?scp=84928982573&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84928982573&partnerID=8YFLogxK

U2 - 10.2140/agt.2015.15.965

DO - 10.2140/agt.2015.15.965

M3 - Article

AN - SCOPUS:84928982573

VL - 15

SP - 965

EP - 986

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

SN - 1472-2747

IS - 2

ER -