DOIAbstract
AbstractWe define a complex R/J of graded modules on ad-dimensional simplicial complex Δ, so that the top homology module of this complex consists of piecewise polynomial functions (splines) of smoothnessron the cone of Δ. In a series of papers,4;5;6] used a similar approach to study the dimension of the spaces of splines on Δ, but with a complex substantially different from R/J. We obtain bounds on the dimension of the homology modulesHi(R/J) for alli<dand find a spectral sequence which relates these modules to the spline module. We use this to give simple conditions governing the projective dimension of the spline module. We also prove that if the spline module is free, then it is determined entirely by local data; that is, by the arrange...
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