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

Laércio Aparecido Lucas, Osamu Saeki

研究成果: ジャーナルへの寄稿学術誌査読

2 被引用数 (Scopus)

抄録

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.

本文言語英語
ページ(範囲)447-462
ページ数16
ジャーナルPacific Journal of Mathematics
207
2
DOI
出版ステータス出版済み - 12月 2002

!!!All Science Journal Classification (ASJC) codes

  • 数学 (全般)

フィンガープリント

「Embeddings of Sp × Sq × Sr in Sp+q+r+1」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。

引用スタイル