## 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 μ invariants, to examine the question of when the double branched cover of a 3 or 4 strand pretzel link embeds.

Original language | English |
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Pages (from-to) | 559-595 |

Number of pages | 37 |

Journal | Transactions of the American Mathematical Society |

Volume | 367 |

Issue number | 1 |

Publication status | Published - 2015 |

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