Immersions of spheres and algebraically constructible functions
Algebraic Geometry
2007-05-23 v1
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.
Cite
@article{arxiv.0704.3523,
title = {Immersions of spheres and algebraically constructible functions},
author = {Iwona Karolkiewicz and Aleksandra Nowel and Zbigniew Szafraniec},
journal= {arXiv preprint arXiv:0704.3523},
year = {2007}
}