Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9516998 | Topology and its Applications | 2005 | 11 Pages |
Abstract
Let f:SpÃSqÃSrâSp+q+r+1 be a smooth embedding with 1⩽p⩽q⩽r. For p⩾2, the authors have shown that if p+qâ r, or p+q=r and r is even, then the closure of one of the two components of Sp+q+r+1âf(SpÃSqÃSr) is diffeomorphic to the product of two spheres and a disk, and that otherwise, there are infinitely many embeddings, called exotic embeddings, which do not satisfy such a property. In this paper, we study the case p=1 and construct infinitely many exotic embeddings. We also give a positive result under certain (co)homological hypotheses on the complement. Furthermore, we study the case (p,q,r)=(1,1,1) more in detail and show that the closures of the two components of S4âf(S1ÃS1ÃS1) are homeomorphic to the exterior of an embedded solid torus or Montesinos' twin in S4.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Laércio Aparecido Lucas, Osamu Saeki,