Embeddings of Sp× Sq× Srin Sp+q+r+1

Laércio Aparecido Lucas, Osamu Saeki
2002 Pacific Journal of Mathematics  
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 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,
more » ... is standard, provided that q < r.
doi:10.2140/pjm.2002.207.447 fatcat:carcw4ay7jfwtjc7niuej5zj5i