Algebraic Invariants for Bestvina-brady Groups
نویسندگان
چکیده
Bestvina-Brady groups arise as kernels of length homomorphisms GΓ → Z from right-angled Artin groups to the integers. Under some connectivity assumptions on the flag complex ∆Γ, we compute several algebraic invariants of such a group NΓ, directly from the underlying graph Γ. As an application, we give examples of finitely presented Bestvina-Brady groups which are not isomorphic to any Artin group or arrangement group.
منابع مشابه
Pushing fillings in right-angled Artin groups
We define a family of quasi-isometry invariants of groups called higher divergence functions, which measure isoperimetric properties “at infinity.” We give sharp upper and lower bounds on the divergence functions for right-angled Artin groups, using different pushing maps on the associated cube complexes. In the process, we define a class of RAAGs we call orthoplex groups, which have the proper...
متن کاملBestvina-Brady Groups and the Plus Construction
A recent result of Bestvina and Brady [1], Theorem 8.7, shows that one of two outstanding questions has a negative answer: either there exists a group of cohomological dimension 2 and geometric dimension 3 (a counterexample to the Eilenberg-Ganea Conjecture [4]), or there exists a nonaspherical subcomplex of an aspherical 2-complex (a counterexample to the Whitehead Conjecture [11]). More preci...
متن کاملCohomology computations for Artin groups, Bestvina–Brady groups, and graph products
We compute: the cohomology with group ring coefficients of Artin groups (or actually, of their associated Salvetti complexes), of Bestvina–Brady groups of type FP, and of graph products of groups, theL-Betti numbers of Bestvina–Brady groups of type FP overQ, and of graph products of groups, the weighted L-Betti numbers of graph products of Coxeter groups. In the case of arbitrary graph products...
متن کاملm at h . A G ] 1 5 Ju l 2 00 6 QUASI - KÄHLER BESTVINA - BRADY GROUPS
A finite simple graph Γ determines a right-angled Artin group GΓ, with one generator for each vertex v, and with one commutator relation vw = wv for each pair of vertices joined by an edge. The Bestvina-Brady group NΓ is the kernel of the projection GΓ → Z, which sends each generator v to 1. We establish precisely which graphs Γ give rise to quasi-Kähler (respectively, Kähler) groups NΓ. This y...
متن کاملQuasi-kähler Bestvina-brady Groups
A finite simple graph Γ determines a right-angled Artin group GΓ, with one generator for each vertex v, and with one commutator relation vw = wv for each pair of vertices joined by an edge. The Bestvina-Brady group NΓ is the kernel of the projection GΓ → Z, which sends each generator v to 1. We establish precisely which graphs Γ give rise to quasi-Kähler (respectively, Kähler) groups NΓ. This y...
متن کامل