Smoothing 3-manifolds in 5-manifolds

2023/09/27 by Michelle Daher, Mark Powell, Daher, Michelle +1
Mathematics · Computer Science · #Geometric and Algebraic Topology #Topological and Geometric Data Analysis #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.2309.15962

Abstract

We show that every locally flat topological embedding of a 3-manifold in a smooth 5-manifold is homotopic, by a small homotopy, to a smooth embedding. We deduce that topologically locally flat concordance implies smooth concordance for smooth surfaces in smooth 4-manifolds.

Related

• Locally flat embeddings of 3-manifolds in S⁴
• A note on embeddings of 3-manifolds in symplectic 4-manifolds
• Constructing locally flat surfaces in 4-manifolds
• Trisections of 5-manifolds
• Constructions of Smooth 4-Manifolds