Nanotubes might not have enought strength for a space elevator
Space.com article
My opinion is that strength will depend heavily on how they are woven. Tethers Unlimited already have a fishnet ribbon tether that can withstand chunks taken out of it by meteorite impacts. Surely this could be done on a microscopic level. And ultimately maybe they can weave carbon nanotorus chain maille. A great deal of strength can be woven into a tether:
