Embedding seifert manifolds in S4

Andrew Donald*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

13 Citations (Scopus)


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 S4. We also find constraints on the Seifert invariants of Seifert 3-manifolds which embed in S4when 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 μ invariants, to examine the question of when the double branched cover of a 3 or 4 strand pretzel link embeds.

Original languageEnglish
Pages (from-to)559-595
Number of pages37
JournalTransactions of the American Mathematical Society
Issue number1
Publication statusPublished - 2015


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