Timeline for Is the Hopf link a Brunnian link?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| Oct 1, 2010 at 18:08 | comment | added | Andrew Stacey | Andre, the actual theorem holds whether or not 1 is prime, you just have to rephrase it to "where the factors are primes greater than 1". So it's convention backed up by the fact that more theorems are about "primes other than 1" than "primes together with 1". In some situations, it's irritating that 2 is a prime! "For any odd prime" is quite a common phrase, but not common enough to warrant new terminology. Anyway, that's quite irrelevant to the actual question. | |
| Oct 1, 2010 at 18:03 | vote | accept | Andrew Stacey | ||
| Oct 1, 2010 at 15:18 | comment | added | André Henriques | The number 1 is definitely NOT prime. Otherwise, the uniqueness of prime factorizations would fail (and the prime factorization of 1 involves zero primes). | |
| Oct 1, 2010 at 14:07 | comment | added | Ryan Budney | H. Debrunner's "Uber den zerfall von verkettungen" Math. Z. 85 (1964) 154-168 and T. Kanenobu's "Hyperbolic links with Brunnian properties" J. Math. Soc. Japan. Vol 38 No. 2 (1986) 295-308. Are about as close to definitive sources on this as you could ask for. I think perhaps more degenerate would be the debate on whether any knot is considered a Brunnian link. | |
| Oct 1, 2010 at 11:51 | answer | added | Jim Conant | timeline score: 7 | |
| Oct 1, 2010 at 11:01 | comment | added | Andrew Stacey | Maybe the correct phrasing should have been to replace "so I suspect" by "in" in the sense that the connection between the questions is very tenuous and only really in the sense that it's a matter of convention (backed up by actual use) rather than any particular deep mathematics. | |
| Oct 1, 2010 at 10:32 | comment | added | S. Carnahan♦ | I feel like the question of whether 1 is prime is more analogous to the question of whether any knot, or the empty manifold, is Brunnian. | |
| Oct 1, 2010 at 8:34 | history | asked | Andrew Stacey | CC BY-SA 2.5 |