Cohomological rigidity for Fano Bott manifolds

Cohomological Rigidity of Real Bott Manifolds

Abstract. A real Bott manifold is the total space of iterated RP 1 bundles starting with a point, where each RP 1 bundle is projectivization of a Whitney sum of two real line bundles. We prove that two real Bott manifolds are diffeomorphic if their cohomology rings with Z/2 coefficients are isomorphic. A real Bott manifold is a real toric manifold and admits a flat riemannian metric invariant u...

Cohomological Non-rigidity of Generalized Real Bott Manifolds of Height 2

We investigate when two generalized real Bott manifolds of height 2 have isomorphic cohomology rings with Z/2 coefficients and also when they are diffeomorphic. It turns out that cohomology rings with Z/2 coefficients do not distinguish those manifolds up to diffeomorphism in general. This gives a counterexample to the cohomological rigidity problem for real toric manifolds posed in [5]. We als...

Classification of Real Bott Manifolds

A real Bott manifold is the total space of a sequence of RP 1 bundles starting with a point, where each RP 1 bundle is the projectivization of a Whitney sum of two real line bundles. A real Bott manifold is a real toric manifold which admits a flat riemannian metric. An upper triangular (0, 1) matrix with zero diagonal entries uniquely determines such a sequence of RP 1 bundles but different ma...

Topological Rigidity for Hyperbolic Manifolds

Let M be a complete Riemannian manifold having constant sectional curvature —1 and finite volume. Let M denote its Gromov-Margulis manifold compactification and assume that the dimension of M is greater than 5. (If M is compact, then M = M and dM is empty.) We announce (among other results) that any homotopy equivalence h: (N,dN) —• (M,dM), where N is a compact manifold, is homotopic to a homeo...

Mirror Symmetry and Fano Manifolds