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Autori: S. Papadima, A.I. Suciu
Editorial: Proceedings of the London Mathematical Society, 100 (3), p.795-834, 2010.
We investigate the relationship between the geometric Bieri–Neumann–Strebel–Renz invariants of a space (or of a group) and the jump loci for homology with coefficients in rank-1 local systems over a field. We give computable upper bounds for the geometric invariants in terms of the exponential tangent cones to the jump loci over the complex numbers. Under suitable hypotheses, these bounds can be expressed in terms of simpler data, for instance, the resonance varieties associated to the cohomology ring. These techniques yield information on the homological finiteness properties of free abelian covers of a given space and of normal subgroups with abelian quotients of a given group. We illustrate our results in a variety of geometric and topological contexts, such as toric complexes and Artin kernels, as well as Kähler and quasi-Kähler manifolds.
Cuvinte cheie: Characteristic variety, Alexander variety, resonance variety, exponential tangent cone, homology of free abelian covers, Bieri-Neumann-Strebel-Renz invariant, Novikov homology, valuation, algebraic integer, right-angled Artin group, Artin kernel, Kähler manifold, quasi-Kähler manifold