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A norm for the cohomology of 2-complexes. (English) Zbl 1014.57002

Summary: We introduce a norm on the real 1-cohomology of finite 2-complexes determined by the Euler characteristics of graphs on these complexes. We also introduce twisted Alexander-Fox polynomials of groups and show that they give rise to norms on the real 1-cohomology of groups. Our main theorem states that for a finite 2-complex \(X\), the norm on \(H^1(X;\mathbb R)\) determined by graphs on \(X\) majorates the Alexander-Fox norms derived from \(\pi_1(X)\).

MSC:

57M20 Two-dimensional complexes (manifolds) (MSC2010)
57M05 Fundamental group, presentations, free differential calculus
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References:

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