Embeddings of Sp × Sq × Sr in Sp+q+r+1

Laércio Aparecido Lucas, Osamu Saeki

研究成果: Contribution to journalArticle査読

2 被引用数 (Scopus)


Let f: Sp × Sq × Sr → Sp+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 Sp+q+r+1 - f(Sp × Sq × Sr), denoted by C1, is diffeomorphic to Sp × Sq × Dr+1 or Sp × Dq+1 × Sr or Dp+1 × Sq × Sr, 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 Sp × Sq × Sr into Sp+q+r+1 and, using the above result, we prove that if C1 has the homology of Sp × Sq, then f is standard, provided that q < r.

ジャーナルPacific Journal of Mathematics
出版ステータス出版済み - 12 2002

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

フィンガープリント 「Embeddings of S<sup>p</sup> × S<sup>q</sup> × S<sup>r</sup> in S<sup>p+q+r+1</sup>」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。