منابع مشابه
Algebraically Constructible Functions
An algebraic version of Kashiwara and Schapira's calculus of constructible functions is used to describe local topological properties of real algebraic sets, including Akbulut and King's numerical conditions for a stratiied set of dimension three to be algebraic. These properties, which include generalizations of the invariants modulo 4, 8, and 16 of Coste and Kurdyka, are deened using the link...
متن کاملDescription of algebraically constructible functions
The algebraically constructible functions on a real algebraic set are the sums of signs of polynomials on this set. We prove a formula giving the minimal number of polynomials needed to write generically a given algebraically constructible function as a sum of signs. We also prove a characterization of the polynomials appearing in a generic presentation of the function with the minimal number o...
متن کاملAlgebraically Constructible Functions and Signs of Polynomials
Let W be a real algebraic set. We show that the following families of integervalued functions on W coincide: (i) the functions of the form w → χ(Xw), where Xw are the fibres of a regular morphism f : X → W of real algebraic sets, (ii) the functions of the form w → χ(Xw), where Xw are the fibres of a proper regular morphism f : X →W of real algebraic sets, (iii) the finite sums of signs of polyn...
متن کاملConstructible motivic functions and motivic integration
1.1. In this paper, intended to be the first in a series, we lay new general foundations for motivic integration and give answers to some important issues in the subject. Since its creation by Maxim Kontsevich [23], motivic integration developed quickly and has spread out in many directions. In a nutshell, in motivic integration, numbers are replaced by geometric objects, like virtual varieties...
متن کاملAlgebraically Constructible Functions: Real Algebra and Topology
Algebraically constructible functions connect real algebra with the topology of algebraic sets. In this survey we present some history, definitions, properties, and algebraic characterizations of algebraically constructible functions, and a description of local obstructions for a topological space to be homeomorphic to a real algebraic set. More than three decades ago Sullivan proved that the l...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2014
ISSN: 0166-8641
DOI: 10.1016/j.topol.2014.10.016