Algebraic invariants for Bestvina-Brady groups

Abstract

Bestvina-Brady groups arise as kernels of length homomorphisms from right-angled Artin groups G_\G to the integers. Under some connectivity assumptions on the flag complex Δ_\G, we compute several algebraic invariants of such a group N_\G, directly from the underlying graph \G. As an application, we give examples of Bestvina-Brady groups which are not isomorphic to any Artin group or arrangement group.

22 pages, accepted for publication in the Journal of the London Mathematical Society

References in corpus (6)

• Algebraic invariants for right-angled Artin groups
• Chen Lie algebras
• When does the associated graded Lie algebra of an arrangement group decompose?
• Quasi-Kähler Bestvina-Brady groups
• The cohomology of Bestvina-Brady groups
• On the CAT(0) dimension of 2-dimensional Bestvina-Brady groups

Cited by in corpus (17)

• Algebraic invariants for right-angled Artin groups
• Toric complexes and Artin kernels
• When does the associated graded Lie algebra of an arrangement group decompose?
• Geometric and algebraic aspects of 1-formality
• Quasi-Kähler Bestvina-Brady groups
• Algebraic monodromy and obstructions to formality
• Abelian duality and propagation of resonance
• Reduced resonance schemes and Chen ranks
• Homology of subgroups of right-angled Artin groups
• Formality and finiteness in rational homotopy theory
• Identifying Dehn Functions of Bestvina--Brady Groups From Their Defining Graphs
• Milnor fibrations of arrangements with trivial algebraic monodromy
• Abelian Splittings and JSJ-Decompositions of Bestvina--Brady Groups
• Alexander invariants and cohomology jump loci in group extensions
• Coabelian ideals in $\mathbb{N}$-graded Lie algebras and applications to right angled Artin Lie algebras
• Complete classification of the Dehn functions of Bestvina-Brady groups
• Isomorphisms Between Bestsvina--Brady Groups and Right-angled Artin Groups