Embedding Seifert Fibred 3-Manifolds and Sol3-Manifolds in 4-Space

1998/05/01 by JS Crisp, JA Hillman · 2 citations
Mathematics · Medicine · #Embedding #Euler characteristic #Fibered knot #Geometric and Algebraic Topology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Knot (papermaking) #Knot theory #Mathematics #Ophthalmology and Eye Disorders #Pure mathematics #Seifert surface #Skein relation

paper · doi:10.1112/s0024611598000379

openalex publication_date 1998/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22

Abstract

We determine strong constraints on the generalized Euler invariants of Seifert bundles over non-orientable base orbifolds which may embed as topologically locally flat submanifolds of S4. In particular, a circle bundle over a non-orientable surface F embeds if and only if it embeds as the boundary of a regular neighbourhood of an embedding of F in S4, and we show that precisely thirteen geometric 3-manifolds with elementary amenable fundamental groups embed. With the exception of the Poincaré homology sphere, each member of the latter class may be obtained by 0-framed surgery on a link which is the union of two slice links, and so embeds smoothly in S4. 1991 Mathematics Subject Classification: 57N13.

Cited by

• Embedding lens spaces in definite 4-manifolds
• The linking pairings of orientable Seifert manifolds

Related

• Locally flat embeddings of 3-manifolds in S⁴
• Embedding Seifert manifolds in S⁴
• Smoothly embedding Seifert fibered spaces in S⁴
• Seifert Manifolds
• Seiberg-Witten Invariants, Alexander Polynomials, and Fibred Classes