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:
“A distinction of property results from that very protection which a free Government gives to unequal faculties of acquiring it.”
—James Madison (1751–1836)
“Social improvement is attained more readily by a concern with the quality of results than with the purity of motives.”
—Eric Hoffer (1902–1983)
“There is not a single rule, however plausible, and however firmly grounded in epistemology, that is not violated at some time or other. It becomes evident that such violations are not accidental events, they are not results of insufficient knowledge or of inattention which might have been avoided. On the contrary, we see that they are necessary for progress.”
—Paul Feyerabend (1924–1994)