Chen ranks and resonance

Abstract

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.

final version, to appear in Advances in Mathematics; erroneous proof of Thm. 5.1 in published version corrected

References in corpus (4)

• Algebraic invariants for right-angled Artin groups
• The integral cohomology of the group of loops
• Geometric and algebraic aspects of 1-formality
• Resonance of basis-conjugating automorphism groups

Cited by in corpus (9)

• The pure braid groups and their relatives
• Pure virtual braids, resonance, and formality
• Chen ranks and resonance varieties of the upper McCool groups
• Recent results on cohomology jump loci
• Reduced resonance schemes and Chen ranks
• Taylor expansions of groups and filtered-formality
• Milnor fibrations of arrangements with trivial algebraic monodromy
• Alexander invariants and cohomology jump loci in group extensions
• On webs, polylogarithms and cluster algebras