Immersions of spheres and algebraically constructible functions
نویسندگان
چکیده
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 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...
متن کاملOn locally constructible spheres and balls
Durhuus and Jonsson (1995) introduced the class of “locally constructible” (LC) 3-spheres and showed that there are only exponentially-many combinatorial types of simplicial LC 3-spheres. Such upper bounds are crucial for the convergence of models for 3D quantum gravity. We characterize the LC property for d-spheres (“the sphere minus a facet collapses to a (d − 2)-complex”) and for d-balls. In...
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ژورنال
عنوان ژورنال: manuscripta mathematica
سال: 2008
ISSN: 0025-2611,1432-1785
DOI: 10.1007/s00229-008-0227-2