I'm trying to fill a woeful gap in my topological knowledge and learn a little knot and link theory (I'll be recording my progress on the nLab, starting with a page on links). Not wishing to write anything incorrect, I found myself with the following question:

Is the Hopf link a Brunnian link?

According to Wikipedia, a Brunnian link is a link with the property that removing any component produces an unlink (of the appropriate size). That's certainly true of the Hopf link! One could outlaw the Hopf link on size grounds and add "of at least 3 components" to the definition of a Brunnian link, but then the family of rubberband Brunnian links is missing its first member (actually, its second; but the first is a fancy way of drawing the unlink).

This feels a bit like the question "Is 1 prime?" so I suspect that the answer is purely a matter of convention but as I'm not a knot theorist, I don't know what the convention is. So I'm hoping that one Steeped in the Depths of Knot Theory can help me out.

conventionbacked 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. – Loop Space Oct 1 '10 at 18:08