  In the Chern-Simons gauge theory formulation of the spinning (2+1)
dimensional black hole, we may treat the horizon and the spatial infinity as
boundaries. We obtain the actions induced on both boundaries, applying the
Faddeev and Shatashvili procedure. The action induced on the boundary of the
horizon is precisely the gauged $SL(2,R)/U(1)$ Wess-Zumino-Witten (WZW) model,
which has been studied previously in connection with a Lorentz signature black
hole in (1+1) dimensions. The action induced on the boundary of spatial
infinity is also found to be a gauged $SL(2,R)$ WZW model, which is equivalent
to the Liouville model, the covariant action for the (1+1) dimensional quantum
gravity. Thus, the (2+1) dimensional black hole is intimately related to the
quantum gravity in (1+1) dimensions.
