We propose a dictionary between geometry of triangulated 3-manifolds and
physics of three-dimensional N=2 gauge theories. Under this duality, standard
operations on triangulated 3-manifolds and various invariants thereof
(classical as well as quantum) find a natural interpretation in field theory.
For example, independence of the SL(2) Chern-Simons partition function on the
choice of triangulation translates to a statement that S^3_b partition
functions of two mirror 3d N=2 gauge theories are equal. Three-dimensional N=2
field theories associated to 3-manifolds can be thought of as theories that
describe boundary conditions and duality walls in four-dimensional N=2 SCFTs,
thus making the whole construction functorial with respect to cobordisms and
gluing.