Cohomology jump loci of 3-manifolds

Abstract

The cohomology jump loci of a space $X$ are of two basic types: the characteristic varieties, defined in terms of homology with coefficients in rank one local systems, and the resonance varieties, constructed from information encoded in either the cohomology ring, or an algebraic model for $X$. We explore here the geometry of these varieties and the delicate interplay between them in the context of closed, orientable 3-dimensional manifolds and link complements. The classical multivariable Alexander polynomial plays an important role in this analysis. As an application, we derive some consequences regarding the formality and the existence of finite-dimensional models for such 3-manifolds.

32 pages; accepted for publication in Manuscripta Mathematica

References in corpus (7)

• Algebraic invariants for right-angled Artin groups
• Boundary manifolds of projective hypersurfaces
• The boundary manifold of a complex line arrangement
• Alexander polynomials: Essential variables and multiplicities
• An introduction to the abelian Reidemeister torsion of three-dimensional manifolds
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Cited by in corpus (2)

• Sigma-invariants and tropical varieties
• Fourier transforms and integer homology cobordism