Algebraic & Geometric Topology

Invariance of Pontrjagin classes for Bott manifolds

Suyoung Choi, Mikiya Masuda, and Satoshi Murai

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Abstract

A Bott manifold is the total space of some iterated 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 2–trivial, where a Bott manifold is called 2–trivial if its cohomology ring with 2–coefficients is isomorphic to that of a product of copies of 1.

Article information

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

Dates
Received: 6 May 2014
Revised: 15 September 2014
Accepted: 18 September 2014
First available in Project Euclid: 28 November 2017

Permanent link to this document
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

Subjects
Primary: 57R19: Algebraic topology on manifolds 57R20: Characteristic classes and numbers

Keywords
Bott manifold cohomological rigidity Pontrjagin class torus manifold $\Z_2$–trivial Bott manifold

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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