Comparison of stratified-algebraic and topological K-theory

Wojciech Kucharz and Krzysztof Kurdyka

Journal of Singularities
volume 22 (2020), 321-336

Received: 20 January 2019.

DOI: 10.5427/jsing.2020.22t

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Abstract:

Stratified-algebraic vector bundles on real algebraic varieties have many desirable features of algebraic vector bundles but are more flexible. We give a characterization of the compact real algebraic varieties X having the following property: There exists a positive integer r such that for any constant rank topological vector bundle ξ on X, the direct sum of r copies of ξ is isomorphic to a stratified-algebraic vector bundle. In particular, each compact real algebraic variety of dimension at most 8 has this property. Our results are expressed in terms of K-theory.

2010 Mathematical Subject Classification:

14P25, 14F25, 19A49, 57R22

Key words and phrases:

Real algebraic variety, stratification, stratified-algebraic vector bundle, stratified-regular map

Author(s) information:

Wojciech Kucharz
Institute of Mathematics
Faculty of Mathematics and Computer Science
Jagiellonian University
ul. Łojasiewicza 6
30-348 Kraków
Poland
email: Wojciech.Kucharz@im.uj.edu.pl

Krzysztof Kurdyka
Laboratoire de Mathématiques
UMR 5127 du CNRS
Université Savoie Mont Blanc
Campus Scientifique
73 376 Le Bourget-du-Lac Cedex
France
email: kurdyka@univ-savoie.fr