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 › peer-review

10 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

Access to Document

10.2140/agt.2015.15.965

Fingerprint Dive into the research topics of 'Invariance of pontrjagin classes for bott manifolds'. Together they form a unique fingerprint.

Cite this

@article{d6a8ecbfcef844b98a59249965d3f839,

title = "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.",

author = "Suyoung Choi and Mikiya Masuda and Satoshi Murai",

year = "2015",

month = apr,

day = "22",

doi = "10.2140/agt.2015.15.965",

language = "English",

volume = "15",

pages = "965--986",

journal = "Algebraic and Geometric Topology",

issn = "1472-2747",

publisher = "Agriculture.gr",

number = "2",

}

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 -