All compact manifolds are homeomorphic to totally algebraic real algebraic sets
type: Item
instance of: scholarly article
title: All compact manifolds are homeomorphic to totally algebraic real algebraic sets
zbMATH Open document ID: 0731.14037
DOI: 10.1007/BF02566639
author: Selman Akbulut
author: Henry C. King
published in: Commentarii Mathematici Helvetici
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/140226
review text: A real algebraic set V is said to be totally algebraic if every \({\mathbb{Z}}/2{\mathbb{Z}}\) homology class of V is represented by a compact algebraic subset. In this paper, the authors prove that any closed smooth manifold is homeomorphic to a totally algebraic real algebraic set. It should be noted that this algebraic set is in general singular; this might appear to diminish the usefulness of the result, but in practice one can often resolve the singularities and apply existing approximation theorems to the resolved manifold to obtain the results one wants. The proofs use blowing-up techniques developed in previous papers of the authors. [For some other recent results of these authors, see Bull. Am. Math. Soc., New Ser. 23, No.2, 441-446 (1990; Zbl 0723.14039)].
reviewed by: P. E. Newstead
Mathematics Subject Classification ID: 14P05
Mathematics Subject Classification ID: 57R99
zbMATH DE Number: 4208275
zbMATH Keywords: totally algebraic real algebraic set
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4208275