Invariance of pontrjagin classes for bott manifolds

Suyoung Choi; Mikiya Masuda; Satoshi Murai

doi:10.2140/agt.2015.15.965

Invariance of pontrjagin classes for bott manifolds

Suyoung Choi, Mikiya Masuda, Satoshi Murai

Research output: Contribution to journal › Article

8 Citations (Scopus)

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.

Original language	English
Pages (from-to)	965-986
Number of pages	22
Journal	Algebraic and Geometric Topology
Volume	15
Issue number	2
DOIs	https://doi.org/10.2140/agt.2015.15.965
Publication status	Published - 2015 Apr 22
Externally published	Yes

ASJC Scopus subject areas

Geometry and Topology

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Choi, S., Masuda, M., & Murai, S. (2015). Invariance of pontrjagin classes for bott manifolds. Algebraic and Geometric Topology, 15(2), 965-986. https://doi.org/10.2140/agt.2015.15.965

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