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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
Bibliography
1 J W Alexander, On the subdivision of a $3$–space by a polyhedron, Proc. Nat. Acad. Sci. USA 10 (1924) 6
2 M Brown, A proof of the generalized Schoenflies theorem, Bull. Amer. Math. Soc. 66 (1960) 74 MR0117695
3 R H Fox, On the imbedding of polyhedra in $3$-space, Ann. of Math. $(2)$ 49 (1948) 462 MR0026326
4 R Z Goldstein, Piecewise linear unknotting of $S^{p}\times S^{q}$ in $S^{p+q+1}$, Michigan Math. J. 14 (1967) 405 MR0220299
5 A Katanaga, O Saeki, Embeddings of quaternion space in $S^4$, J. Austral. Math. Soc. Ser. A 65 (1998) 313 MR1660419
6 M A Kervaire, J W Milnor, Groups of homotopy spheres. I, Ann. of Math. $(2)$ 77 (1963) 504 MR0148075
7 S Kinoshita, On Fox's property of a surface in a $3$-manifold, Duke Math. J. 33 (1966) 791 MR0203720
8 A Kosiński, On Alexander's theorem and knotted spheres, from: "Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961)", Prentice-Hall (1962) 55 MR0158369
9 L A Lucas, O M Neto, O Saeki, A generalization of Alexander's torus theorem to higher dimensions and an unknotting theorem for $S^p\times S^q$ embedded in $S^{p+q+2}$, Kobe J. Math. 13 (1996) 145 MR1442202
10 L A Lucas, O Saeki, Diffeomorphisms of a product of spheres and embedded spheres, Topology Appl. 123 (2002) 471 MR1924046
11 L A Lucas, O Saeki, Embeddings of $S^p\times S^q\times S^r$ in $S^{p+q+r+1}$, Pacific J. Math. 207 (2002) 447 MR1972255
12 L A Lucas, O Saeki, Codimension one embeddings of product of three spheres, Topology Appl. 146/147 (2005) 409 MR2107160
13 J H Rubinstein, Dehn's lemma and handle decompositions of some $4$-manifolds, Pacific J. Math. 86 (1980) 565 MR590570
14 S Smale, Generalized Poincaré's conjecture in dimensions greater than four, Ann. of Math. $(2)$ 74 (1961) 391 MR0137124
15 S Suzuki, On a complexity of a surface in $3$-sphere, Osaka J. Math. 11 (1974) 113 MR0346791
16 C T C Wall, Killing the middle homotopy groups of odd dimensional manifolds, Trans. Amer. Math. Soc. 103 (1962) 421 MR0139185
17 C T C Wall, Unknotting tori in codimension one and spheres in codimension two, Proc. Cambridge Philos. Soc. 61 (1965) 659 MR0184249