#### Volume 11, issue 5 (2011)

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The Fox property for codimension one embeddings of products of three spheres into spheres

### Laércio Aparecido Lucas and Osamu Saeki

Algebraic & Geometric Topology 11 (2011) 3043–3064
##### Abstract

Fox has shown that for every closed connected surface smoothly embedded in ${S}^{3}$, the closure of each component of its complement is diffeomorphic to the closure of the complement of a handlebody embedded in ${S}^{3}$. In this paper, we study a similar “Fox property” for smooth embeddings of ${S}^{p}×{S}^{q}×{S}^{r}$ in ${S}^{p+q+r+1}$.

##### Keywords
embedding, product of spheres, codimension one, exterior
Primary: 57R40
Secondary: 57Q45