  We re-examine the physical origin of the polymer glass transition from the
point of view of marginal rigidity, which is achieved above a certain number of
intermolecular contacts. In the case of polymer chains in a melt / poor
solvent, each monomer has two neighbors bound by covalent bonds and also a
number of central-force contacts modelled by the Lennard-Jones (LJ) potential.
We find that when the average number of contacts per monomer (covalent and
non-covalent) exceeds the critical value z*=4, the system becomes solid and the
dynamics arrested - a state that we declare the glass. Coarse-grained Brownian
dynamics simulations show that at sufficient strength of LJ attraction (which
effectively represents the depth of quenching, or the quality of solvent) the
polymer globule indeed crosses the threshold of z*=4, and does become a glass.
We verify this by showing the distinction between the `liquid' polymer droplet
at z<z*, which changes shape and adopts the spherical conformation in
equilibrium, and the `glassy' droplet at z>z*, which retains its shape frozen
at the moment of z* crossover. These results provide a robust working criterion
to tell the liquid apart from the glass for the linear polymers.
