Non-Abelian Resonance: Product and Coproduct Formulas

  • Ştefan Papadima
  • Alexander I. Suciu
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 96)


We investigate the resonance varieties attached to a commutative differential graded algebra and to a representation of a Lie algebra, with emphasis on how these varieties behave under finite products and coproducts.


Resonance variety Differential graded algebra Lie algebra product Coproduct 



This work was started while the two authors visited the Max Planck Institute for Mathematics in Bonn in April–May 2012. The work was pursued while the second author visited the Institute of Mathematics of the Romanian Academy in June 2012 and June 2013, and MPIM Bonn in September–October 2013. Thanks are due to both institutions for their hospitality, support, and excellent research atmosphere.


  1. 1.
    Chen, K.-T.: Extension of C function algebra by integrals and Malcev completion of π 1. Adv. Math. 23, 181–210 (1977)CrossRefMATHGoogle Scholar
  2. 2.
    Dimca, A., Papadima, S.: Nonabelian cohomology jump loci from an analytic viewpoint. Comm. Contemp. Math. 16(4), 1350025 (2014)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Dimca, A., Papadima, S., Suciu, A.: Topology and geometry of cohomology jump loci. Duke Math. J. 148(3), 405–457 (2009)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Goldman, W., Millson, J.: The deformation theory of representations of fundamental groups of compact Kähler manifolds. Inst. Hautes Études Sci. Publ. Math. 67, 43–96 (1988)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Măcinic, A., Papadima, S., Popescu, R., Suciu, A.: Flat connections and resonance varieties: from rank one to higher ranks. Preprint arXiv:1312.1439v2 Google Scholar
  6. 6.
    Papadima, S., Suciu, A.: Bieri–Neumann–Strebel–Renz invariants and homology jumping loci. Proc. Lond. Math. Soc. 100(3), 795–834 (2010).MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Papadima, S., Suciu, A.: Jump loci in the equivariant spectral sequence. Math. Res. Lett. 21(4), arXiv:1302.4075v3 (2014)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Simion Stoilow Institute of MathematicsBucharestRomania
  2. 2.Department of MathematicsNortheastern UniversityBostonUSA

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