Break upon striking a hard object? It's possible to construct monomolecular edges today, but they aren't particularly useful, because the sharper the edge, the faster it dulls, and a blade that is no longer sharp after penetrating a micrometer into armor isn't particularly helpful.
The thinnest edges normally made are multiple molecules thick, but properly chipped glass can be monomolecular, and many fibers are long-chain molecules (carbon nanotubes are molecular tubes, and very strong for their thickness, but not really a factor for cutting weapons, and a single tube would still require so little force to snap you would not be aware you'd hit it). The problem is that, really, a monomolecular edge isn't very useful; real monomolecular fibers aren't strong enough unless you bunch a whole lot of them together, and assuming you came up with some super-filaments that were strong enough to cut through normal materials, there's an obvious defense -- just line your armor with a grid of the same filaments.
Well, duh. That's called an arms race!
