  Using a mapping of compact polymers on the Manhattan lattice to spanning
trees, we calculate exactly the average number of bends at infinite
temperature. We then find, in a high temperature approximation, the energy of
the system as a function of bending rigidity and polymer elasticity. We
identify the universal mechanism for the relaxation of compact polymers and
then endow the model with physically motivated dynamics in the convenient
framework of the trees. We find aging and domain coarsening after quenches in
temperature. We explain the slow dynamics in terms of the geometrical
interconnections between the energy and the dynamics.
