Mappings into the Stiefel manifold and cross-cap singularities

Iwona Krzyżanowska; Aleksandra Nowel

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arXiv · 1507.04892

Mappings into the Stiefel manifold and cross-cap singularities

Iwona Krzyżanowska·Aleksandra Nowel

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Abstract

Take n>k>1 such that n-k is odd. In this paper we consider mapping a from (n-k+1)-dimensional closed ball into the space of (n \times k)--matrices such that its restriction to a sphere goes into the Stiefel manifold V_k(R^n). We construct a homotopy invariant \Lambda\ of a|S^{n-k} which defines an isomorphism between (n-k)-th group of homotopy of V_k(\R^n) and Z_2. It can be used to calculate in an effective way the class of a|S^{n-k} in this homotopy group for a polynomial mapping a and to find the number mod 2 of cross-cap singularities of a mapping from a closed m-dimensional ball into R^{2m-1}, m even.

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BibTeX RIS

Iwona Krzyżanowska, Aleksandra Nowel. 2015-07-17. Mappings into the Stiefel manifold and cross-cap singularities. https://arxiv.org/abs/1507.04892

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