Date of Award:
5-1971
Document Type:
Thesis
Degree Name:
Master of Science (MS)
Department:
Mathematics and Statistics
Department name when degree awarded
Mathematics
Committee Chair(s)
L. D. Loveland
Committee
L. D. Loveland
Abstract
The central theme for this paper is provided by the following three statements:
(1) Every compact connected 1-manifold is S1.
(2) Every compact connected simply connected 2-manifold is S2.
(3) Every compact connected simply connected 3-manifold is S3.
We provide proofs of statements (1) and (2). The veracity of the third statement, the Poincaré Conjecture, has not been determined. It is known that should a counter-example exist it can be found by removing from S3 a finite collect ion of solid tori and sewing them back differently. We show that it is not possible to find a counterexample by removing from S3 a single solid torus of twist knot type or torus knot type and sewing it back differently. We treat as special cases a solid torus of trivial knot type and trefoil knot type.
Checksum
0563f559c1c73fc76c72093025c57d74
Recommended Citation
Peck, Joseph D., "The Poincaré Conjecture" (1971). All Graduate Theses and Dissertations, Spring 1920 to Summer 2023. 6850.
https://digitalcommons.usu.edu/etd/6850
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