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Journal für die reine und angewandte Mathematik

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Volume 2018, Issue 745


Stratified-algebraic vector bundles

Wojciech Kucharz
  • Institute of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30-348 Kraków, Poland
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/ Krzysztof Kurdyka
  • Laboratoire de Mathématiques, UMR CNRS 5127, Université Savoie Mont-Blanc, Campus Scientifique, 73 376 Le Bourget-du-Lac Cedex, France
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Published Online: 2016-03-01 | DOI: https://doi.org/10.1515/crelle-2015-0105


We investigate stratified-algebraic vector bundles on a real algebraic variety X. A stratification of X is a finite collection of pairwise disjoint, Zariski locally closed subvarieties whose union is X. A topological vector bundle ξ on X is called a stratified-algebraic vector bundle if, roughly speaking, there exists a stratification 𝒮 of X such that the restriction of ξ to each stratum S in 𝒮 is an algebraic vector bundle on S. In particular, every algebraic vector bundle on X is stratified-algebraic. It turns out that stratified-algebraic vector bundles have many surprising properties, which distinguish them from algebraic and topological vector bundles.


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About the article

Received: 2014-09-11

Revised: 2015-10-26

Published Online: 2016-03-01

Published in Print: 2018-12-01

The first author was partially supported by NCN (Poland) grant 2011/01/B/ST1/01289. The second author was partially supported by ANR (France) grant STAAVF.

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2018, Issue 745, Pages 105–154, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2015-0105.

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