Strong Cohomological rigidity of Bott manifolds
Suyoung Choi, Taekgyu Hwang, Hyeontae Jang
TL;DR
This paper proves that for Bott manifolds, any isomorphism of their cohomology rings corresponds to a diffeomorphism, confirming the strong cohomological rigidity conjecture.
Contribution
It establishes the validity of the strong cohomological rigidity conjecture specifically for Bott manifolds, linking algebraic isomorphisms to geometric diffeomorphisms.
Findings
Any graded cohomology ring isomorphism between two Bott manifolds is induced by a diffeomorphism.
Confirms the strong cohomological rigidity conjecture for Bott manifolds.
Provides a complete classification of Bott manifolds via their cohomology rings.
Abstract
We show that the strong cohomological rigidity conjecture for Bott manifolds is true. Namely, any graded cohomology ring isomorphism between two Bott manifolds is induced by a diffeomorphism.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis