Non-abelian cohomology jump loci from an analytic viewpoint (Q2876615)

In the article [\textit{W. M. Goldman} and \textit{J. J. Millson}, Publ. Math., Inst. Hautes Étud. Sci. 67, 43--96 (1988; Zbl 0678.53059)], analytic germs of representation varieties are studied, via the deformation theory of flat connections on differentiable manifolds. The paper under review aims at an extension of the corresponding theory to topological spaces, using the basic properties of the characteristic and resonance varieties (introduced earlier in the context of commutative differential graded algebras [\textit{A. Dimca} et al., Duke Math. J. 148, No. 3, 405--457 (2009; Zbl 1222.14035)]), the investigation of the cohomology jump loci of spaces, certain properties of \textit{D. Sullivan}'s minimal models [Publ. Math., Inst. Hautes Étud. Sci. 47, 269--331 (1977; Zbl 0374.57002)] and relations with the theory of Malcev Lie algebras, and so on. The authors also apply the developed approach to the investigation of formal spaces, quasi-projective manifolds, finitely generated nilpotent groups, etc.