Polynomial mappings into a Stiefel manifold and immersions

2011/11/17 by Krzyżanowska, Iwona, Szafraniec, Zbigniew
#14P25 #57R42 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1111.4030

Abstract

For a polynomial mapping from S^n-k to the Stiefel manifold \widetildeV_k(\Rⁿ), where n-k is even, there is presented an effective method of expressing the corresponding element of the homotopy group π_n-k\widetildeV_k(\Rⁿ)≃\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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