On the Imbedding of Polyhedra in 3-Space

Abstract

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Embeddings of quaternion space in S4

“…REMARK 2.4. We can also obtain a similar result in the smooth category, provided that we replace S 4 by homotopy 4-spheres.…”

“…The second result of this paper is an affirmative answer to this question for a large class of embedded projective planes (see Corollary 3.3); for example, if either P x or P 2 is the connected sum of the standardly embedded projective plane in S 4 (see [12,19]) with a locally flat 2-knot (see [7][8][9]), then the answer is affirmative. The paper is organized as follows.…”

“…Pi are topologically locally flatly embedded projective planes in S 4 . We consider the following problem: does there exist a locally flat topological embedding f : Q -> S 4 …”

“…We consider the following problem: does there exist a locally flat topological embedding f : Q -> S 4 …”

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

“…S 3 splits S 3 into two handlebodies. Fox [3] has shown that for every smooth embedding f W F ! S 3 , the closure of each of the two components of S 3 X f .F / is diffeomorphic to the closure of the complement of a handlebody embedded in S 3 .…”