SPIN-STRUCTURES ON REAL BOTT MANIFOLDS

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...

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...

Classification of Real Bott Manifolds and Acyclic Digraphs

We completely characterize real Bott manifolds up to diffeomorphism in terms of three simple matrix operations on square binary matrices obtained from strictly upper triangular matrices by permuting rows and columns simultaneously. We also prove that any graded ring isomorphism between the cohomology rings of real Bott manifolds with Z/2 coefficients is induced by an affine diffeomorphism betwe...

Weak Spin(9)-structures on 16-dimensional Riemannian Manifolds

TORSION INVARIANTS OF Spin c - STRUCTURES ON 3 - MANIFOLDS

Recently there has been a surge of interest in the Seiberg-Witten invariants of 3-manifolds, see [3], [4], [7]. The Seiberg-Witten invariant of a closed oriented 3-manifold M is a function SW from the set of Spin-structures on M to Z. This function is defined under the assumption b1(M) ≥ 1 where b1(M) is the first Betti number of M ; in the case b1(M) = 1 the function SW depends on the choice o...