Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-27T07:34:03.410Z Has data issue: false hasContentIssue false
  • English
  • Français

Embedding Seifert fibred 3-manifolds andSol3-manifolds in 4-space

Published online by Cambridge University Press:  01 May 1998

JS Crisp  and
JA Hillman
JS Crisp
Affiliation:
Present address: Faculty of Mathematical Studies, University of Southampton, Southampton SO17 1BJ, UK.
Get access

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 $S^4$. 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 $S^4$, 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 $S^4$.

1991 Mathematics Subject Classification: 57N13.

Keywords

embeddinghypersurfaceSeifert fibred 3-manifold$\mbox{\em Sol\/}^3$-manifoldslice linksurgery
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 76 , Issue 3 , May 1998 , pp. 685 - 710
Copyright
London Mathematical Society 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)