Embedding 3-manifolds with circle actions in 4-space


J. A. Hillman


Research Report 98-10
Date: 21 April 1998


We show that if M is an orientable 3-manifold which is Seifert fibred over an orientable base orbifold B and which embeds in \Bbb{R}^4 then the generalized Euler invariant of the fibration is determined up to sign by B unless H_1(M;\Bbb{Z}) is torsion free, in which case it can take at most one nonzero value (up to sign). In particular, no such manifold with 3 exceptional fibres and Euler invariant 0 embeds in \Bbb{R}^4.

Key phrases

embedding. Euler invariant. linking pairing. Seifert bundle.

AMS Subject Classification (1991)

Primary: 57N10
Secondary: 57N13.


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