  A quantitative understanding of the microscopic constraints which underlie a
well relaxed glassy structure is the key to developing a microscopic theory of
structural evolution and plasticity for the amorphous solid. Here we
demonstrate the applicability of one such theory of local bonding constraints
developed by D. R. Nelson [Phys. Rev. B 28, 5515 (1983)], for a model binary
Lennard-Jones glass structure that has undergone an isothermal annealing
simulation spanning over 10 micro-seconds of physical simulation time. By
introducing a modified radical Voronoi tessellation which removes some
ambiguity in how nearest neighbour bonds are enumerated, it is found, that a
large proportion ($>95\%$) of local atomic environments follow the connectivity
rules of the SU(2) topology of Nelson's work resulting in a dense network of
disclination lines characterizing the defect bonds. Furthermore, it is
numerically shown that a low energy glass structure corresponds to a reduced
level of bond-length frustration and thus a minimally defected bond-defect
network. It is then demonstrated that such a defect network provides a
framework in which to analyse thermally-activated structural excitations,
revealing those high-energy/low-density regions not following the connectivity
constraints are more likely to undergo structural rearrangement that often
results in a local relaxation that ends with the creation of new SU(2) local
topology content.
