Splines with boundary conditions

This paper explores spaces of splines satisfying boundary conditions using the long exact sequence for relative homology. We relate them to the boundary complex of ΔΔ, where ΔΔ is a planar simplicial complex which triangulates a pseudomanifold. In this case, there is a natural relationship between the Hilbert polynomials (which measure the dimension of Ckr(Δ̂) for k≫0k≫0) of the spline modules.