L_∞-cohomology and metabolicity of negatively curved complexes

We prove the analog of de Rham's theorem for l_∞-cohomology of the universal cover of a finite simplicial complex. A sufficient criterion is given for linearity of isoperimetric functions for filling cycles of any positive dimension over ℝ. This implies the linear higher dimensional isoperimetric inequalities for the fundamental groups of finite negatively curved complexes and of closed negatively curved manifolds. Also, these groups are ℝ-metabolic.