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arXiv · 0704.3523

Immersions of spheres and algebraically constructible functions

Iwona Karolkiewicz·Aleksandra Nowel·Zbigniew Szafraniec
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Abstract

Let L be an algebraic set and let g : R^(n+1) \times L --> R^(2n) (n is even) be a polynomial mapping such that for each l in L there is r(l)>0 such that the mapping g_l = g(.,l) restricted to the sphere S^n(r) is an immersion for every 0<r<(l), so that the intersection number I(g_l|S^n(r)) is defined. Then the function which maps l in L to I(g_l|S^n(r)) is algebraically constructible.

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Iwona Karolkiewicz, Aleksandra Nowel, Zbigniew Szafraniec. 2007-04-26. Immersions of spheres and algebraically constructible functions. https://arxiv.org/abs/0704.3523

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