Applications of algebraic topology in bounding the rank of the skew-symmetric curvature operator
Let \(V\) an inner product space of signature \((p,q)\), let \(R\) be an algebraic curvature tensor on \(V\) and let \(R(\cdot)\) be the associated skew-symmetric operator. Assume that the rank of \(R(\cdot)\) is equal to a constant \(r\) on the Grassmannian of nondegenerate 2 planes. Using Stiefel-Whitney classes and \(K\)-theory, the author shows that \(r=2\) if \(p=0\), 1 and \(q\geq 9\) or if \(p=2\) and if \(q\geq 10\) and if \(q\) and \(q+2\) are not powers of 2.
scientific article; zbMATH DE number 1879078
scientific article