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
VL - 15
SP - 965
EP - 986
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
SN - 1472-2747
IS - 2
ER -