Orientable manifolds with nonzero dual Stiefel-Whitney classes of largest possible grading
Abstract
It is known that, for all n, there exist compact differentiable orientable n-manifolds with dual Stiefel-Whitney class wbarn-ahat(n) nonzero, and this is best possible, but the proof is nonconstructive. Here ahat(n) equals the number of 1's in the binary expansion of n if n equiv 1 mod 4 and exceeds this by 1 otherwise. We find, for all n nonzero mod 4, examples of real Bott manifolds with this property.
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