Spin manifolds with nonzero dual Stiefel-Whitney classes of large grading
Donald M. Davis
Abstract
The dual Stiefel-Whitney classes wbarj(M) of a manifold M are elements of Hj(M;Z/2) which give information about embedding and immersing M in Euclidean space. We consider the question of finding, for each n, the largest j such that there is an n-dimensional Spin manifold with wbarj nonzero. We obtain upper and lower bounds. Since one theorem proves existence of manifolds without giving explicit examples, we consider a parallel question of finding explicit manifolds with wbarj nonzero for j as large as possible.
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