  We construct from first principles the operator 'A-hat' that annihilates the
partition functions (or wavefunctions) of three-dimensional Chern-Simons theory
with gauge groups SU(2), SL(2,R), or SL(2,C) on a knot complement M. The
operator 'A-hat' is a quantization of the knot complement's classical
A-polynomial A(l,m). The construction proceeds by decomposing three-manifolds
into ideal tetrahedra, and invoking a new, more global understanding of gluing
in TQFT to put them back together. We advocate in particular that, properly
interpreted, "gluing = symplectic reduction." We also arrive at a new
finite-dimensional state integral model for computing the analytically
continued "holomorphic blocks" that compose any physical Chern-Simons partition
function.
