A concordance analogue of the 4-dimensional light bulb theorem

2019/03/07 by Maggie Miller, Miller, Maggie
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1903.03055

openalex publication_date 2019/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a concordance analogue of Gabai's 4-dimensional light bulb theorem. That is, we show that when R and R' are homotopically (smoothly) embedded 2-spheres in a 4-manifold X⁴ where π₁(X⁴) has no 2-torsion and one of R or R' has a transverse sphere, then R and R' are concordant. When π₁(X⁴) has 2-torsion, we give a similar statement with extra hypotheses as in the 4-dimensional light bulb theorem. We also give similar statements when R and R' are orientable positive-genus surfaces.

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