Embedding 3-manifolds with circle actions in 4-space

Author

J. A. Hillman

Status

Research Report 98-10
Date: 21 April 1998

Abstract

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.

Content

The paper is available in the following forms:

TeX dvi format:: 1998-10.dvi.gz (13kB) or 1998-10.dvi (28kB)
PostScript:: 1998-10.ps.gz (34kB) or 1998-10.ps (107kB)

To minimize network load, please choose the smaller gzipped .gz form if and only if your browser client supports it.

Sydney Mathematics and Statistics