Chen ranks and resonance

Daniel C. Cohen, Henry K. Schenck

Research output: Contribution to journalArticlepeer-review


The Chen groups of a group G are the lower central series quotients of the maximal metabelian quotient of G. Under certain conditions, we relate the ranks of the Chen groups to the first resonance variety of G, a jump locus for the cohomology of G. In the case where G is the fundamental group of the complement of a complex hyperplane arrangement, our results positively resolve Suciu's Chen ranks conjecture. We obtain explicit formulas for the Chen ranks of a number of groups of broad interest, including pure Artin groups associated to Coxeter groups, and the group of basis-conjugating automorphisms of a finitely generated free group.

Original languageEnglish (US)
Pages (from-to)1-27
Number of pages27
JournalAdvances in Mathematics
StatePublished - Nov 5 2015


  • Chen group
  • Hyperplane arrangement
  • Primary
  • Resonance variety
  • Secondary

ASJC Scopus subject areas

  • Mathematics(all)

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