Embedding Seifert manifolds in the 4-sphere


John S. Crisp


Research Report 94-39
Date: 17 November 1994


The G-signature theorem is used to obtain a relative bound on the rational Euler invariant of any Seifert manifold M, over a nonorientable closed surface, which embeds in 4-space. This bound is sharp whenever the singular fibres of M are all odd and occur in pairs of opposite sign, and in the case of genuine circle bundles we obtain a complete classification of those which embed. The torsion linking form is computed explicity for a Seifert manifold M over a nonorientable closed surface, and conditions are found for this to be hyperbolic, thereby giving extra necessary conditions for embedding M in the 4-sphere.

Key phrases

Seifert manifold. embedding. 4-sphere. G-signature theorem. torsion linking.

AMS Subject Classification (1991)

Primary: 57N10
Secondary: 57N35, 57N13


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