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Embedding Seifert manifolds in $ S^4$

Author: Andrew Donald
Journal: Trans. Amer. Math. Soc. 367 (2015), 559-595
MSC (2010): Primary 57R40; Secondary 57M25
Published electronically: September 5, 2014
MathSciNet review: 3271270
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Abstract: Using an obstruction based on Donaldson's theorem on the intersection forms of definite 4-manifolds, we determine which connected sums of lens spaces smoothly embed in $ S^4$. We also find constraints on the Seifert invariants of Seifert 3-manifolds which embed in $ S^4$ when either the base orbifold is non-orientable or the first Betti number is odd. In addition, we construct some new embeddings and use these, along with the $ d$ and $ \overline {\mu }$ invariants, to examine the question of when the double branched cover of a 3 or 4 strand pretzel link embeds.

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Additional Information

Andrew Donald
Affiliation: School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QW, United Kingdom
Address at time of publication: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824

Received by editor(s): March 20, 2013
Published electronically: September 5, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.