Equivariant semialgebraic vector bundles
type: Item
instance of: scholarly article
title: Equivariant semialgebraic vector bundles
zbMATH Open document ID: 1027.14028
DOI: 10.1016/S0166-8641(01)00291-7
author: Myung-Jun Choi
author: Tomohiro Kawakami
author: Dae Heui Park
published in: Topology and its Applications
publication date: 2002-09-17T00:00:00Z
review text: The authors prove that every semialgebraic \(G\)-vector bundle over a semialgebraic \(G\)-set \(E\) has a semialgebraic classifying \(G\)-map and moreover that the set of semialgebraic \(G\)-isomorphism classes of semialgebraic \(G\)-vector bundles over \(E\) corresponds bijectively to the set of topological \(G\)-isomorphism classes of topological \(G\)-vector bundles over \(E\). An interesting application of these theorems is the equivariant semialgebraic version of the homotopy property for semialgebraic \(G\)-vector bundles proven in the final part of the paper.
reviewed by: Zbigniew Hajto
Mathematics Subject Classification ID: 14P10
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 14P20
Mathematics Subject Classification ID: 55Q91
zbMATH DE Number: 1801773
zbMATH Keywords: semialgebraic \(G\)-set
zbMATH Keywords: semialgebraic \(G\)-vector bundle
zbMATH Keywords: Nash \(G\)-vector bundle
zbMATH Keywords: transformation group
zbMATH Keywords: equivariant semialgebraic homotopy
MaRDI profile type: Publication
cites work: The equivariant covering homotopy property for differentiable G-fibre bundles
cites work: Q3770650
cites work: Q3704110
cites work: Semialgebraic topology over a real closed field. II: Basic theory of semialgebraic spaces
cites work: Separation, retractions and homotopy extension in semialgebraic spaces
cites work: Q3471225
cites work: Q4313558
cites work: Q4248688
cites work: Equivariant bundles
cites work: One-dimensional Nash groups
cites work: Q3998356
cites work: Equivariant semialgebraic homotopies
cites work: Equivariant K-theory
cites work: Approximation Theorems for Nash Mappings and Nash Manifolds
cites work: Nash manifolds
full work available at URL: s0166-8641(01)00291-7
OpenAlex ID: W1994832251
description: scientific article; zbMATH DE number 1801773