On approximating submanifolds by algebraic sets and a solution to the Nash conjecture

DOI10.1007/BF01231882zbMath0781.14038WikidataQ123010042 ScholiaQ123010042MaRDI QIDQ1187479

Selman Akbulut, Henry C. King

Publication date: 22 July 1992

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143958

zbMATH Keywords

approximation of smooth manifolds by real algebraic setsdeformations of smooth immersions into algebraic onesisotopic to a nonsingular algebraic setNash conjecture

Mathematics Subject Classification ID

Real algebraic sets (14P05) Topology of real algebraic varieties (14P25) Real-analytic and Nash manifolds (58A07) Real-analytic sets, complex Nash functions (32C07)

Related Items (20)

Algebraic Cycles and Approximation Theorems in Real Algebraic Geometry ⋮ Some conjectures on continuous rational maps into spheres ⋮ Noncompact codimension-1 real algebraic manifolds ⋮ Continuous rational maps into spheres ⋮ Algebraic obstructions and a complete solution of a rational retraction problem ⋮ Algebraic realization for simple groups ⋮ Algebraic realization of actions of some finite groups ⋮ Some new results on the topology of nonsingular real algebraic sets ⋮ Strongly algebraic realization of dihedral group actions ⋮ Algebraic approximation of analytic subsets of \(\mathbb C^q\times\{0\}\) in \(\mathbb C^{q+1}\) ⋮ Algebraic realization for cyclic group actions with one isotropy type ⋮ Approximation and homotopy in regulous geometry ⋮ Algebraic realization for cyclic group actions ⋮ Nash’s work in algebraic geometry ⋮ Approximation by continuous rational maps into spheres ⋮ Algebraicity of cycles on smooth manifolds ⋮ Higher order approximation of analytic sets by topologically equivalent algebraic sets ⋮ Examples of algebraically realized maps ⋮ Higher order approximation of complex analytic sets by algebraic sets ⋮ Rational maps in real algebraic geometry

Cites Work

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• Real algebraic structures on topological spaces
• Any compact differentiable submanifold of \({\mathbb{R}}^ n\) has an algebraic approximation in \({\mathbb{R}}^ n\)
• The topology of real algebraic sets with isolated singularities
• Algebraicity of immersions in \(\mathbb{R}^ n\)
• Approximating submanifolds of real projective space by varieties
• Real algebraic manifolds
• Algebraic Approximation of Manifolds
• Submanifolds and Homology of Nonsingular Real Algebraic Varieties
• Singular Points of Complex Hypersurfaces. (AM-61)

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