منابع مشابه
Algebraic boundaries of convex semi-algebraic sets
We study the algebraic boundary of a convex semi-algebraic set via duality in convex and algebraic geometry. We generalise the correspondence of facets of a polytope with the vertices of the dual polytope to general semi-algebraic convex sets. In this case, exceptional families of extreme points might exist and we characterise them semi-algebraically. We also give a strategy for computing a com...
متن کاملSemi-algebraic neighborhoods of closed semi-algebraic sets
— Given a closed (not necessarly compact) semi-algebraic set X in Rn, we construct a non-negative semi-algebraic C2 function f such that X=f−1(0) and such that for δ > 0 sufficiently small, the inclusion of X in f−1([0, δ]) is a retraction. As a corollary, we obtain several formulas for the Euler characteristic of X. Résumé. — Étant donné un ensemble semi-algébrique fermé (non nécessairement co...
متن کاملSemi-algebraic Geometry of Braid Groups
The braid group of n-strings is the group of homotopy types of movements of n distinct points in the 2-plane R. It was introduced by E. Artin [1] in 1926 in order to study knots in R. He gave a presentation of the braid group by generators and relations, which are, nowadays, called the Artin braid relations. Since then, not only in the study of knots, the braid groups appear in several contexts...
متن کاملReal Homotopy Theory of Semi-algebraic Sets
We complete the details of a theory outlined by Kontsevich and Soibelman that associates to a semi-algebraic set a certain graded commutative differential algebra of “semi-algebraic differential forms” in a functorial way. This algebra encodes the real homotopy type of the semialgebraic set in the spirit of the DeRham algebra of differential forms on a smooth manifold. Its development is needed...
متن کاملComputing Roadmaps of General Semi-Algebraic Sets
In this paper we study the problem of determining whether two points lie in the same connected component of a semi-algebraic set S. Although we are mostly concerned with sets S , our algorithm can also decide if points in an arbitrary set S R can be joined by a semi-algebraic path, for any real closed eld R. Our algorithm computes a one-dimensional semi-algebraic subset <(S) of S (actually of a...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 1992
ISSN: 0373-0956
DOI: 10.5802/aif.1291