Cubes with Knotted Holes,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1971
- Accession Number
- AD0722357
Entities
People
- J. M. Martin
- R. H. Bing
Organizations
- University of Wisconsin–Madison