Knot Theory 2: Reidemester to the Rescue

I'm going to try to explain this next bit without any pictures. That may be a mistake; the texts I've seen on the subject all come profusely supplied with diagrams. In particular, the "Reidemeister moves" I try to describe below are usually depicted rather than described. I hope I've made things clear enough; if not, it may help to play around a bit with rubber bands and bits of string. (If it still isn't clear, feel free to complain; I'm willing to try again...)

( From Three To Two )

Deep breath

Okay. With that in place, we can go on to the problem of constructing invariants. Stay tuned, if you're still interested.