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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 S3, the closure of each component of its complement is diffeomorphic to the closure of the complement of a handlebody embedded in S3. In this paper, we study a similar “Fox property” for smooth embeddings of Sp × Sq × Sr in Sp+q+r+1.

Keywords

embedding, product of spheres, codimension one, exterior
Mathematical Subject Classification

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/