## Abstract

We give geometric formulae which enable us to detect (completely in some cases) the regular homotopy class of an immersion with trivial normal bundle of a closed oriented 3-manifold into 5-space. These are analogues of the geometric formulae for the Smale invariants due to Ekholm and the second author. As a corollary, we show that two embeddings into 5-space of a closed oriented 3-manifold with no 2-torsion in the second cohomology are regularly homotopic if and only if they have Seifert surfaces with the same signature. We also show that there exist two embeddings F_{0} and F_{8} : T^{3} right arrow-hooked R^{5} of the 3-torus T^{3} with the following properties: (1) F_{0}#h is regularly homotopic to F_{8} for some immersion h : S^{3} right arrow, looped R^{5}, and (2) the immersion h as above cannot be chosen from a regular homotopy class containing an embedding.

Original language | English |
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Pages (from-to) | 13-32 |

Number of pages | 20 |

Journal | Manuscripta Mathematica |

Volume | 108 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2002 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)