#### 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
##### Publication
Received: 26 February 2011
Revised: 3 October 2011
Accepted: 6 October 2011
Published: 22 December 2011
##### Authors
 Laércio Aparecido Lucas Academia da Força Aérea Alameda dos Pinheiros, 4315 13632-490 Pirassununga, SP Brazil Osamu Saeki Institute of Mathematics for Industry Kyushu University Motooka 744, Nishi-ku Fukuoka 819-0395 Japan http://imi.kyushu-u.ac.jp/~saeki/