Strong cohomological rigidity of Hirzebruch surface bundles in Bott towers

TL;DR

This paper proves that the cohomological structure uniquely determines Hirzebruch surface bundles over Bott manifolds, confirming the strong cohomological rigidity conjecture for certain high-dimensional Bott manifolds.

Contribution

It establishes the strong cohomological rigidity of Hirzebruch surface bundles in Bott towers, advancing the understanding of topological invariants in complex geometry.

Findings

Strong cohomological rigidity for Hirzebruch surface bundles

Confirmation of the conjecture for 8-dimensional Bott manifolds

Implications for classification of complex manifolds

Abstract

We show the strong cohomological rigidity of Hirzebruch surface bundles over Bott manifolds. As a corollary, we have that the strong cohomological rigidity conjecture is true for Bott manifolds of dimension $8$.