TY - JOUR

T1 - Invariance of pontrjagin classes for bott manifolds

AU - Choi, Suyoung

AU - Masuda, Mikiya

AU - Murai, Satoshi

N1 - Publisher Copyright:
© 2015, Algebraic & Geometric Topology. All Rights Reserved.

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.

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U2 - 10.2140/agt.2015.15.965

DO - 10.2140/agt.2015.15.965

M3 - Article

AN - SCOPUS:84928982573

SN - 1472-2747

VL - 15

SP - 965

EP - 986

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

IS - 2

ER -