Accession Number : AD0722357

Title :   Cubes with Knotted Holes,

Corporate Author : WISCONSIN UNIV MADISON

Personal Author(s) : Bing,R. H. ; Martin,J. M.

Report Date : APR 1971

Pagination or Media Count : 26

Abstract : The 3-dimensional Poincare conjecture is that a compact, connected, simply connected 3-manifold without boundary is topologically a 3-sphere S sup 3. Despite efforts to prove the conjecture, it has withstood attack. It is known that every orientable 3-manifold may be obtained by removing a collection of disjoint solid tori from S sup 3 and sewing them back differently. In this paper the author examine some of the possibilities for constructing a counterexample to the Poincare conjecture by removing a single solid torus from S sup 3 and sewing it back differently. Actually, they examine not only this process but one analogous to it which they call 'attaching a pillbox to a cube with a knotted hole.' (Author)

Descriptors :   (*ALGEBRAIC TOPOLOGY, GROUPS(MATHEMATICS)), THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE