  It is shown that three-dimensional systems of coupled quantum wires support
fractional topological phases composed of closed loops and open planes of
two-dimensional fractional quantum Hall subsystems. These phases have
topologically protected edge states, and are separated by exotic quantum phase
transitions corresponding to a rearrangement of fractional quantum Hall edge
modes. Some support for the existence of an extended exotic critical phase
separating the bulk gapped fractional topological phases is given. Without
electron-electron interactions, similar but unfractionalized bulk gapped phases
based on coupled integer quantum Hall states exist. They are separated by an
extended critical Weyl semimetal phase.
