## Abstract

We give a simple axiomatic definition of a rationalvalued invariant σ(W,V,e) of triples (W,V,e), where W ⊃ V are smooth oriented closed manifolds of dimensions 6 and 3, and e is a second rational cohomology class of the complement W \ V satisfying a certain condition. The definition is stated in terms of cobordisms of such triples and the signature of 4-manifolds. When W = S ^{6} and V is a smoothly embedded 3-sphere, and when e/2 is the Poincaré dual of a Seifert surface of V, the invariant coincides with -8 times Haefliger's embedding invariant of (S ^{6},V). Our definition recovers a more general invariant due to Takase, and contains a new definition for Milnor's triple linking number of algebraically split 3-component links in ℝ ^{3} that is close to the one given by the perturbative series expansion of the Chern-Simons theory of links in ℝ ^{3}.

Original language | English |
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Pages (from-to) | 193-237 |

Number of pages | 45 |

Journal | Journal of Mathematical Sciences |

Volume | 18 |

Issue number | 2 |

Publication status | Published - 2011 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Statistics and Probability
- General Mathematics
- Applied Mathematics