Smoothing maps into algebraic sets and spaces of flat connections

Let X ⊂ R n be a real algebraic set and M a smooth, closed manifold. We show that all continuous maps M → X are homotopic (in X ) to C ∞ maps. We apply this result to study characteristic classes of vector bundles associated to continuous families of complex group representations, and we establish l...

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Bibliographic Details
Published inGeometriae dedicata Vol. 174; no. 1; pp. 359 - 374
Main Authors Baird, Thomas, Ramras, Daniel A.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.02.2015
Subjects
Algebraic Geometry
Convex and Discrete Geometry
Differential Geometry
Hyperbolic Geometry
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Topology
Chern class
55R37
Secondary: 57R20
Maps between classifying spaces
53C05
Real algebraic set
Flat connection
Primary: 14P05
Chern-Weil theory
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Summary:Let X ⊂ R n be a real algebraic set and M a smooth, closed manifold. We show that all continuous maps M → X are homotopic (in X ) to C ∞ maps. We apply this result to study characteristic classes of vector bundles associated to continuous families of complex group representations, and we establish lower bounds on the ranks of the homotopy groups of spaces of flat connections over aspherical manifolds.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-014-0022-z