Le groupe de Witt d'une surface réelle.
This note is based on the lectures that I have given during the winter school Winter Braids IV, School on algebraic and topological aspects of braid groups held in Dijon on 10 - 13 February 2014. The aim of series of three lectures was to give an overview of geometrical and topological properties of 4-dimensional Lefschetz fibrations. Meanwhile, I could briefly introduce real Lefschetz fibrations, fibrations which have certain symmetry, and could present some interesting features of them.This note...
Let be a closed semialgebraic subset of euclidean space of codimension at least one, and containing the origin as a non-isolated point. We prove that, for every real , there exists an algebraic set which approximates to order at . The special case generalizes the result of the authors that every semialgebraic cone of codimension at least one is the tangent cone of an algebraic set.