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Conference Paper

Comparison of stratified-algebraic and topological K-theory

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Kucharz,  Wojciech
Max Planck Institute for Mathematics, Max Planck Society;

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http://dx.doi.org/10.5427/jsing.2020.22t
(Publisher version)

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Citation

Kucharz, W., & Kurdyka, K. (2020). Comparison of stratified-algebraic and topological K-theory. Journal of Singularities, 22, 321-336. doi:10.5427/jsing.2020.22t.


Cite as: https://hdl.handle.net/21.11116/0000-0009-1121-E
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 having the following
property: There exists a positive integer r such that for any topological
vector bundle E on X, the direct sum of r copies of E 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.