On the topology of semi-algebraic functions on closed semi-algebraic sets
Algebraic Geometry
2010-12-10 v1
Abstract
We consider a semi-algebraic function defined on a closed semi-algebraic set X. We give formulas relating the topology of X to the indices of the critical points of the function and to the topological behavior of the function at infinity. We give applications when X is R^n and when the function is linear.
Keywords
Cite
@article{arxiv.1012.2093,
title = {On the topology of semi-algebraic functions on closed semi-algebraic sets},
author = {Nicolas Dutertre},
journal= {arXiv preprint arXiv:1012.2093},
year = {2010}
}