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
Lucas, Laércio Aparecido 1 ; Saeki, Osamu 2
@article{10_2140_agt_2011_11_3043,
author = {Lucas, La\'ercio Aparecido and Saeki, Osamu},
title = {The {Fox} property for codimension one embeddings of products of three spheres into spheres},
journal = {Algebraic and Geometric Topology},
pages = {3043--3064},
year = {2011},
volume = {11},
number = {5},
doi = {10.2140/agt.2011.11.3043},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2011.11.3043/}
}
TY - JOUR AU - Lucas, Laércio Aparecido AU - Saeki, Osamu TI - The Fox property for codimension one embeddings of products of three spheres into spheres JO - Algebraic and Geometric Topology PY - 2011 SP - 3043 EP - 3064 VL - 11 IS - 5 UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2011.11.3043/ DO - 10.2140/agt.2011.11.3043 ID - 10_2140_agt_2011_11_3043 ER -
%0 Journal Article %A Lucas, Laércio Aparecido %A Saeki, Osamu %T The Fox property for codimension one embeddings of products of three spheres into spheres %J Algebraic and Geometric Topology %D 2011 %P 3043-3064 %V 11 %N 5 %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2011.11.3043/ %R 10.2140/agt.2011.11.3043 %F 10_2140_agt_2011_11_3043
Lucas, Laércio Aparecido; Saeki, Osamu. The Fox property for codimension one embeddings of products of three spheres into spheres. Algebraic and Geometric Topology, Tome 11 (2011) no. 5, pp. 3043-3064. doi: 10.2140/agt.2011.11.3043
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