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

Lucas, Laércio Aparecido; Saeki, Osamu

doi:10.2140/agt.2011.11.3043

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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

DOI: 10.2140/agt.2011.11.3043

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 $S^{p} \times S^{q} \times S^{r}$ in $S^{p + q + r + 1}$ .

Keywords

embedding, product of spheres, codimension one, exterior

Mathematical Subject Classification 2010

Primary: 57R40

Secondary: 57Q45

References

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/

Volume 11, issue 5 (2011)