## Osaka Journal of Mathematics

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

### Filtered cohomological rigidity of bott towers

#### 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