Smoothly embedding Seifert fibered spaces in S⁴

2018/10/10 by Ahmad Issa, Duncan McCoy, Issa, Ahmad +1 · 1 citation
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1810.04770

openalex publication_date 2018/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using an obstruction based on Donaldson's theorem, we derive strong restrictions on when a Seifert fibered space Y = F(e; (p₁)/(q₁), …, (p_k)/(q_k)) over an orientable base surface F can smoothly embed in S⁴. This allows us to classify precisely when Y smoothly embeds provided e > k/2, where e is the normalized central weight and k is the number of singular fibers. Based on these results and an analysis of the Neumann-Siebenmann invariant μ, we make some conjectures concerning Seifert fibered spaces which embed in S⁴. Finally, we also provide some applications to doubly slice Montesinos links, including a classification of the smoothly doubly slice odd pretzel knots up to mutation.

Citations

• Embedding 3-manifolds with circle actions
• Einlagerung von Mannigfaltigkeiten in euklidische R�ume
• Embedding Seifert manifolds in 𝑆⁴
• The Imbedding of Bounding Manifolds in Euclidean Space

Cited by

• On 3-manifolds admitting co-orientable taut foliations, but none with vanishing Euler class

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