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Oct 20, 2010 at 7:44 comment added Greg Kuperberg @Victor Yes, I suppose I did not answer that part of the question. 2 is from a failed proof of the Kepler conjecture, not exactly a pretty proof but at least a proof. 3 shows up from time to time in function field problems.
Jul 17, 2010 at 19:25 comment added Victor Protsak But where are the pretty proofs that go away?
Jul 17, 2010 at 13:28 comment added Greg Kuperberg 3. $F = \mathbb{C}(x)$, $K = \mathbb{C}(x^2)$, $L = \mathbb{C}((x+1)^2)$. Actually there are tons of examples in function field theory. 4. $S^1 \times C_2$, $O(2)$, and (the one that is the easiest to miss) $\text{Pin}^-(2)$, the normalizer of a circle in $\text{SU}(2)$.
Jul 17, 2010 at 13:17 comment added Anweshi What would be a counterexamples for 3? In 4, what is the second Lie group that is diffeomorphic to pair of circles? (the first one is the direct sum of S^1 and Z/2, I assume.)
Jul 17, 2010 at 4:02 history answered Greg Kuperberg CC BY-SA 2.5