  Given a Lie group G whose Lie algebra is endowed with a nondegenerate
invariant symmetric bilinear form, we construct a Poisson algebra of continuous
functions on a certain open subspace R of the space of representations in G of
the fundamental group of a compact connected orientable topological surface
with finitely many boundary circles; when G is compact and connected, R may be
taken dense in the space of all representations. The space R contains spaces of
representations where the values of those generators of the fundamental group
which correspond to the boundary circles are constrained to lie in fixed
conjugacy classes and, on these representation spaces, the Poisson algebra
restricts to stratified symplectic Poisson algebras constructed elsewhere
earlier. Hence the Poisson algebra on R gives a description of the variation of
the stratified symplectic Poisson structures on the smaller representation
spaces as the chosen conjugacy classes move.
