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We show that that classical rational homotopy theory in the sense of Sullivan[6] can be extended compactly supported setting. This presents a simplicialversion of the compactly supported de Rham complex in characteristic zero, andproving that it models singular compactly supported cohomology. This presentsnew avenues of possible study in proper homotopy theory, and further extensionsof the ideas within the classical literature of Quillen [5] and Sullivan.

A commutative model for PL compactly supported cohomology in characteristic zero