# 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

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Sydney Mathematics and Statistics