Accession Number:

AD0722357

Title:

Cubes with Knotted Holes,

Descriptive Note:

Corporate Author:

WISCONSIN UNIV MADISON

Personal Author(s):

Report Date:

1971-04-01

Pagination or Media Count:

26.0

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

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE