  A kind of topological field theory is proposed as a candidate to describe the
global structure of the 2-form Einstein gravity with or without a cosmological
constant. Indeed in the former case, we show that a quantum state in the
candidate gives an exact solution of the Wheeler-DeWitt equation. The BRST
quantization based on the Batalin-Fradkin-Vilkovisky (BFV) formalism is carried
out for this topological version of the 2-form Einstein gravity.
