On smooth approximation of integral cycles mod 2

2025/11/13 by Caldini, Gianmarco
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.10545

Abstract

We prove that every mod 2 integral cycle T in a Riemannian manifold M can be approximated in flat norm by a cycle which is a smooth submanifold Σ of nearly the same area, up to a singular set of codimension 3; in addition, this estimate on the singular set can be refined depending on the codimension of the cycle. Moreover, if the mod 2 homology class τ admits a smooth embedded representative, then Σ can be chosen free of singularities. This article provides the unoriented version of the smooth approximation theorem for integral cycles.

Citations

• Optimal smooth approximation of integral cycles
• Normal and Integral Currents

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