Invariance of pontrjagin classes for bott manifolds

Suyoung Choi, Mikiya Masuda, Satoshi Murai

Research output: Contribution to journalArticle

6 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 languageEnglish
Pages (from-to)965-986
Number of pages22
JournalAlgebraic and Geometric Topology
Volume15
Issue number2
DOIs
Publication statusPublished - 2015 Apr 22
Externally publishedYes

Fingerprint

Invariance
Cohomology Ring
Isomorphism
Graded Ring
Diffeomorphism
Bundle
Trivial
Isomorphic
Class

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

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

In: Algebraic and Geometric Topology, Vol. 15, No. 2, 22.04.2015, p. 965-986.

Research output: Contribution to journalArticle

Choi, Suyoung ; Masuda, Mikiya ; Murai, Satoshi. / Invariance of pontrjagin classes for bott manifolds. In: Algebraic and Geometric Topology. 2015 ; Vol. 15, No. 2. pp. 965-986.
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