## Abstract

Let f: S^{p} × S^{q} × S^{r} → S^{p+q+r+1},2 ≤ p ≤ q ≤ r, be a smooth embedding. In this paper we show that the closure of one of the two components of S^{p+q+r+1} - f(S^{p} × S^{q} × S^{r}), denoted by C_{1}, is diffeomorphic to S^{p} × S^{q} × D^{r+1} or S^{p} × D^{q+1} × S^{r} or D^{p+1} × S^{q} × S^{r}, provided that p + q ≠ r or p + q = r with r even. We also show that when p + q = r with r odd, there exist infinitely many embeddings which do not satisfy the above property. We also define standard embeddings of S^{p} × S^{q} × S^{r} into S^{p+q+r+1} and, using the above result, we prove that if C_{1} has the homology of S^{p} × S^{q}, then f is standard, provided that q < r.

Original language | English |
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Pages (from-to) | 447-462 |

Number of pages | 16 |

Journal | Pacific Journal of Mathematics |

Volume | 207 |

Issue number | 2 |

DOIs | |

Publication status | Published - Dec 2002 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)