Stratified-algebraic vector bundles
Algebraic Geometry
2016-03-17 v1
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.
Cite
@article{arxiv.1308.4376,
title = {Stratified-algebraic vector bundles},
author = {Wojciech Kucharz and Krzysztof Kurdyka},
journal= {arXiv preprint arXiv:1308.4376},
year = {2016}
}