On the link of a stratum in a real algebraic set
type: Item
instance of: scholarly article
title: On the link of a stratum in a real algebraic set
zbMATH Open document ID: 0787.14038
DOI: 10.1016/0040-9383(92)90025-D
author: Krzysztof Kurdyka
author: Michel Coste
published in: Topology
publication date: 1993-01-16T00:00:00Z
review text: Recall, an Euler space is a triangulable space such that the link of every point on it has an even Euler characteristic. Sullivan proved that real algebraic sets are Euler spaces. Later the reviewer and King and also Benedetti and Dedo showed that the converse of this is also true in dimension two. In dimension greater than two the reviewer and King gave examples of Euler spaces that can not be homeomorphic to algebraic sets. They proved that algebraic sets have to satisfy further topological-combinatorial restrictions. In dimension three they gave necessary and sufficient (topological) conditions for a set to be homeomorphic (or isomorphic) to a real algebraic set. The authors give some generalizations of these results. As an application they give an example of an algebraic set, which topologically imbeds into \(\mathbb{R}^ 4\), but cannot be homeomorphic to an algebraic subset of \(\mathbb{R}^ 4\) [see also the discussion of this result by the reviewer and \textit{A. King} in Real algebraic geometry, Proc. Conf., Rennes/Fr. 1991, Lect. Notes Math. 1524, 120-127 (1992; Zbl 0771.14016)].
reviewed by: Selman Akbulut
Mathematics Subject Classification ID: 14P10
Mathematics Subject Classification ID: 57Q15
Mathematics Subject Classification ID: 57Q35
zbMATH DE Number: 89838
zbMATH Keywords: Euler space
zbMATH Keywords: algebraic sets
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 89838