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Cohomology jump loci of 3-manifolds

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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.

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  1. Department of Mathematics, Northeastern University, Boston, MA, 02115, USA

    Alexander I. Suciu

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This work was supported by Simons Foundation Collaboration Grants for Mathematicians #354156 and #693825.

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Suciu, A.I. Cohomology jump loci of 3-manifolds. manuscripta math. 167, 89–123 (2022). https://doi.org/10.1007/s00229-020-01264-5

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