Osaka Journal of Mathematics

Filtered cohomological rigidity of bott towers

Hiroaki Ishida

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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

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1340197937

Mathematical Reviews number (MathSciNet)
MR2945760

Zentralblatt MATH identifier
1250.57041

Subjects
Primary: 57R19: Algebraic topology on manifolds 57R20: Characteristic classes and numbers 57S25: Groups acting on specific manifolds 14M25: Toric varieties, Newton polyhedra [See also 52B20]

Citation

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


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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.