### Abstract

We clarify the structure of the set of regular homotopy classes containing embeddings of a 3-manifold into 5-space inside the set of all regular homotopy classes of immersions with trivial normal bundles. As a consequence, we show that for a large class of 3-manifolds M^{3}, the following phenomenon occurs: there exists a codimension two immersion of the 3-sphere whose double points cannot be eliminated by regular homotopy, but can be eliminated after taking the connected sum with a codimension two embedding of M^{3}. This involves introducing and studying an equivalence relation on the set of spin structures on M^{3}. Their associated μ-invariants also play an important role.

Original language | English |
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Pages (from-to) | 5049-5061 |

Number of pages | 13 |

Journal | Transactions of the American Mathematical Society |

Volume | 354 |

Issue number | 12 |

DOIs | |

Publication status | Published - Dec 1 2002 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

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## Cite this

*Transactions of the American Mathematical Society*,

*354*(12), 5049-5061. https://doi.org/10.1090/S0002-9947-02-03070-2