  We investigate the Hilbert complex of elasticity involving spaces of
symmetric tensor fields. For the involved tensor fields and operators we show
closed ranges, Friedrichs/Poincare type estimates, Helmholtz type
decompositions, regular decompositions, regular potentials, finite cohomology
groups, and, most importantly, new compact embedding results. Our results hold
for general bounded strong Lipschitz domains of arbitrary topology and rely on
a general functional analysis framework (FA-ToolBox). Moreover, we present a
simple technique to prove the compact embeddings based on regular
decompositions/potentials and Rellich's section theorem, which can be easily
adapted to any Hilbert complex.
