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 | |
| Publication status | Published - 2015 Apr 22 |
| Externally published | Yes |
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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 journal › Article
}
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 -