Topology of the resonating valence-bond state: Solitons and high-$T_c$ superconductivity

We study the topological order in the resonating valence-bond state. The elementary excitations have reversed charge-statistics relations: There are neutral spin-1/2 fermions and charge ±e spinless bosons, analogous to the solitons in polyacetylene. The charged excitations are very light, and form a degenerate Bose gas even at high temperatures. We discuss this model in the context of the recently discovered oxide superconductors.