Smoothing maps into algebraic sets and spaces of flat connections
Algebraic Topology
2014-10-14 v4 Algebraic Geometry
Differential Geometry
K-Theory and Homology
Abstract
Let X be a real algebraic subset of R^n and M a smooth, closed manifold. We show that all continuous maps from M to X are homotopic (in X) to C^\infty 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.
Cite
@article{arxiv.1206.3341,
title = {Smoothing maps into algebraic sets and spaces of flat connections},
author = {Thomas Baird and Daniel A. Ramras},
journal= {arXiv preprint arXiv:1206.3341},
year = {2014}
}
Comments
15 pages. To appear in Geometriae Dedicata. Changes in v4: Removed material on the topological Atiyah-Segal map, which will appear in a separate article. Various other small changes to the exposition