Embedding Seifert manifolds in $S^4$
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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.References
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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
- MR Author ID: 1007879
- Email: a.donald.1@research.gla.ac.uk, adonald@math.msu.edu
- Received by editor(s): March 20, 2013
- Published electronically: September 5, 2014
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 367 (2015), 559-595
- MSC (2010): Primary 57R40; Secondary 57M25
- DOI: https://doi.org/10.1090/S0002-9947-2014-06174-6
- MathSciNet review: 3271270