## Osaka Journal of Mathematics

### Filtered cohomological rigidity of bott towers

Hiroaki Ishida

#### Abstract

A Bott tower is an iterated $\mathbb{C}\mathrm{P}^{1}$-bundle over a point, where each $\mathbb{C}\mathrm{P}^{1}$-bundle is the projectivization of a rank $2$ decomposable complex vector bundle. For a Bott tower, the filtered cohomology is naturally defined. We show that isomorphism classes of Bott towers are distinguished by their filtered cohomology rings. We even show that any filtered cohomology ring isomorphism between two Bott towers is induced by an isomorphism of the Bott towers.

#### Article information

Source
Osaka J. Math., Volume 49, Number 2 (2012), 515-522.

Dates
First available in Project Euclid: 20 June 2012

https://projecteuclid.org/euclid.ojm/1340197937

Mathematical Reviews number (MathSciNet)
MR2945760

Zentralblatt MATH identifier
1250.57041

#### Citation

Ishida, Hiroaki. Filtered cohomological rigidity of bott towers. Osaka J. Math. 49 (2012), no. 2, 515--522. https://projecteuclid.org/euclid.ojm/1340197937

#### References

• S. Choi and M. Masuda: Classification of $\mathbb{Q}$-trivial Bott manifolds, preprint, arXiv:math.AT/0912.5000.
• S. Choi, M. Masuda and D.Y. Suh: Topological classification of generalized Bott towers, Trans. Amer. Math. Soc. 362 (2010), 1097–1112.