Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Embedding Seifert manifolds in $ S^4$


Author: Andrew Donald
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
Published electronically: September 5, 2014
MathSciNet review: 3271270
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 57R40, 57M25

Retrieve articles in all journals with MSC (2010): 57R40, 57M25


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
Email: a.donald.1@research.gla.ac.uk, adonald@math.msu.edu

DOI: https://doi.org/10.1090/S0002-9947-2014-06174-6
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.

American Mathematical Society