Bieri–Neumann–Strebel–Renz invariants and homology jumping loci
By Stefan Papadima, Alexander I. Suciu. 2008
66 citations recorded by the source corpus.
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.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/3c4d5582b1e0e14199e0327092685384c8dda118
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- Hyperplane arrangements and Milnor fibrations (2013, background): “Furthermore, as noted in [54], the depth-1 resonance varieties Rq(X, k) = Rq1(X, k) behave well under direct products: R(X1 ×X2, k) = q ⋃”