Real Algebraic and Analytic Geometry

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332. Iwona Krzyzanowska Zbigniew Szafraniec:
Polynomial mappings into a Stiefel manifold and immersions.

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Submission: 2011, November 14.

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 $S^m\rightarrow\R^{2m}$.

Mathematics Subject Classification (2000): 14P25, 57R42.

Keywords and Phrases: Stiefel manifolds, Immersions, Quadratic forms.

Full text, 19p.: dvi 90k, pdf 300k.

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