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1999•International Journal of Algebra and ComputationRequires access

ℓ∞-COHOMOLOGY AND METABOLICITY OF NEGATIVELY CURVED COMPLEXES

Igor Mineyev

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Abstract

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.

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What this paper is about

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.

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OpenAlex reports 5 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

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.

Key concepts: Isoperimetric inequality, Mathematics, Cohomology, Pure mathematics, Cover (algebra), Dimension (graph theory), De Rham cohomology, Mathematical analysis

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