## Algebraic & Geometric Topology

### Invariance of Pontrjagin classes for Bott manifolds

#### Abstract

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 $ℂℙ1$.

#### Article information

Source
Algebr. Geom. Topol., Volume 15, Number 2 (2015), 965-986.

Dates
Revised: 15 September 2014
Accepted: 18 September 2014
First available in Project Euclid: 28 November 2017

https://projecteuclid.org/euclid.agt/1511895795

Digital Object Identifier
doi:10.2140/agt.2015.15.965

Mathematical Reviews number (MathSciNet)
MR3342682

Zentralblatt MATH identifier
1321.57038

#### Citation

Choi, Suyoung; Masuda, Mikiya; Murai, Satoshi. Invariance of Pontrjagin classes for Bott manifolds. Algebr. Geom. Topol. 15 (2015), no. 2, 965--986. doi:10.2140/agt.2015.15.965. https://projecteuclid.org/euclid.agt/1511895795

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