Smoothing maps into algebraic sets and spaces of flat connections

2012/06/14 by Thomas John Baird, Baird, Thomas, Daniel A. Ramras +1 · 1 citation
Mathematics · #14P05 #53C05 (primary) #55R37 (secondary) #57R20 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.1206.3341

openalex publication_date 2012/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a real algebraic subset of Rⁿ and M a smooth, closed manifold. We show that all continuous maps from M to 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.

Cited by

• The Homotopy Type of Spaces of Flat Connections for Classical Lie Groups

Related

• Smooth Homotopy of Infinite-Dimensional C^∞-Manifolds
• The Homotopy Type of Spaces of Flat Connections for Classical Lie Groups
• Spaces of algebraic and continuous maps between real algebraic varieties
• The Rational Homotopy of Stable C_p-Smoothings
• Conditions of smoothness of moduli spaces of flat connections and of character varieties