Polynomial mappings into a Stiefel manifold and immersions

Details Polynomial mappings into a Stiefel manifold and immersions Polynomial mappings into a Stiefel manifold and immersions

2011-11-17

arxiv.org/abs/1111.4030v1

Mathematics

Algebraic Geometry

Scientific paper

For a polynomial mapping from S^{n-k} to the Stiefel manifold \widetilde{V}_k(\R^{n}), where n-k is even, there is presented an effective method of expressing the corresponding element of the homotopy group \pi_{n-k}\widetilde{V}_k(\R^{n})\simeq\Z in terms of signatures of quadratic forms. There is also given a method of computing the intersection number for a polynomial immersion from S^m to \R^{2m}.

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