  I point out an unexpected relation between the BV (Batalin-Vilkovisky) and
the BFV (Batalin-Fradkin-Vilkovisky) formulations of the same pure gauge
(topological) theory. The nonminimal sector in the BV formulation of the
topological theory allows one to construct the Poisson bracket and the BRST
charge on some Lagrangian submanifold of the BV configuration space; this
Lagrangian submanifold can be identified with the phase space of the BFV
formulation of the same theory in the minimal sector of ghost variables. The
BFV Poisson bracket is induced by a natural even Poisson bracket on the
stationary surface of the master action, while the BRST charge originates from
the BV gauge-fixed BRST transformation defined on a gauge-fixing surface. The
inverse construction allows one to arrive at the BV formulation of the
topological theory starting with the BFV formulation. This correspondence gives
an intriguing geometrical interpretation of the nonminimal variables and
clarifies the relation between the Hamiltonian and Lagrangian quantization of
gauge theories.
  This is an extended version of the talk given at the QFTHEP-99 workshop in
Moscow, May 27 -June 2, 1999.
