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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.
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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

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