Embedding Seifert manifolds in S^4

Details Embedding Seifert manifolds in S^4 Embedding Seifert manifolds in S^4

2012-03-27

arxiv.org/abs/1203.6008v1

Mathematics

Geometric Topology

46 pages, 20 figures

Scientific paper

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

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