Results
Every closed, orientable, connected 3-manifold is obtained by performing Dehn surgery on a link in the 3-sphere. This result, the Lickorish-Wallace theorem, was first proven by Wallace in 1960 and independently by Lickorish in a stronger form in 1962. Via the now well-known relation between genuine surgery and cobordism, this result is equivalent to the theorem that the oriented cobordism group of 3-manifolds is trivial, originally due to Vladimir Abramovich Rokhlin in 1951.
Since orientable 3-manifolds can all be generated by suitably decorated links, one might ask how distinct surgery presentations of a given 3-manifold might be related. The answer is called the Kirby calculus.
Read more about this topic: Dehn Surgery
Famous quotes containing the word results:
“How can you tell if you discipline effectively? Ask yourself if your disciplinary methods generally produce lasting results in a manner you find acceptable. Whether your philosophy is democratic or autocratic, whatever techniques you use—reasoning, a “star” chart, time-outs, or spanking—if it doesn’t work, it’s not effective.”
—Stanley Turecki (20th century)
““The ideal reasoner,” he remarked, “would, when he had once been shown a single fact in all its bearings, deduce from it not only all the chain of events which led up to it but also all the results which would follow from it.””
—Sir Arthur Conan Doyle (1859–1930)
“Life and language are alike sacred. Homicide and verbicide—that is, violent treatment of a word with fatal results to its legitimate meaning, which is its life—are alike forbidden.”
—Oliver Wendell Holmes, Sr. (1809–1894)