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Embedding Seifert Fibred 3‐Manifolds and Sol 3 ‐Manifolds in 4‐Space
Author(s) -
Crisp JS,
Hillman JA
Publication year - 1998
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611598000379
Subject(s) - mathematics , fibered knot , embedding , homology (biology) , euler characteristic , pure mathematics , knot (papermaking) , seifert surface , knot theory , skein relation , biochemistry , chemistry , artificial intelligence , chemical engineering , computer science , engineering , gene
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.