Vol. 32, No. 2, 1970

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Unknotting unions of cells

Thomas Benny Rushing

Vol. 32 (1970), No. 2, 521–525

In this note we consider the problem of determining whether the union of cells is nicely embedded in the n-sphere if each of the cells is nicely embedded. This question is related to many embedding problems. For instance, the n-dimensional Annulus Conjecture (now known to be true for n4) is a special case. Cantrell and Lacher have shown that an affirmative answer implies local flatness of certain submanifolds. Also, this question is related to the conjecture that an embedding of a complex into the n-sphere which is locally flat on open simplexes is e-tame in codimension three.

Mathematical Subject Classification
Primary: 57.01
Secondary: 55.00
Received: 15 April 1969
Published: 1 February 1970
Thomas Benny Rushing