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arXiv · 1308.4376

Stratified-algebraic vector bundles

Wojciech Kucharz·Krzysztof Kurdyka
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Abstract

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 on X is called a stratified-algebraic vector bundle if, roughly speaking, there exists a stratification of X such that the restriction of the bundle to each stratum is an algebraic vector bundle. 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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Wojciech Kucharz, Krzysztof Kurdyka. 2013-08-20. Stratified-algebraic vector bundles. https://doi.org/10.1515/crelle-2015-0105

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