Abstract
AbstractWe present a complete functional formula expressing theith ℤ2-Betti number of the oriented Grassmann manifold of oriented 3-dimensional vector subspaces in Euclideann-space forifrom the range determined by the characteristic rank of the canonical oriented 3-dimensional vector bundle over this manifold. The same formula explicitly exhibits the number of linearly independent semi-invariants of degree 3 of a binary form of degreen− 3. Using the approach and data presented in this note, analogous results can be obtained for the oriented Grassmann manifold of oriented 4-dimensional vector subspaces in Euclideann-space and semi-invariants of degree 4 of a binary form of degreen− 4.
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