We compute the BNS-invariant for the pure symmetric automorphism groups of right-angled Artin groups. We use this calculation to show that the pure symmetric automorphism group of a right-angled Artin group is itself not a right-angled Artin group pr
ovided that its defining graph contains a separating intersection of links.
In 1987 Bieri, Neumann and Strebel introduced a geometric invariant for discrete groups. In this article we compute and explicitly describe the BNS-invariant for the pure braid groups.
In this paper, we compute the {Sigma}^n(G) and {Omega}^n(G) invariants when 1 rightarrow H rightarrow G rightarrow K rightarrow 1 is a short exact sequence of finitely generated groups with K finite. We also give sufficient conditions for G to have t
he R_{infty} property in terms of {Omega}^n(H) and {Omega}^n(K) when either K is finite or the sequence splits. As an application, we construct a group F rtimes? Z_2 where F is the R. Thompsons group F and show that F rtimes Z_2 has the R_{infty} property while F is not characteristic.
We compute the {Omega}^1(G) invariant when 1 {to} H {to} G {to} K {to} 1 is a split short exact sequence. We use this result to compute the invariant for pure and full braid groups on compact surfaces. Applications to twisted conjugacy classes and to
finite generation of commutator subgroups are also discussed.
In this note, we compute the {Sigma}^1(G) invariant when 1 {to} H {to} G {to} K {to} 1 is a short exact sequence of finitely generated groups with K finite. As an application, we construct a group F semidirect Z_2 where F is the R. Thompsons group F
and show that F semidirect Z_2 has the R-infinity property while F is not characteristic. Furthermore, we construct a finite extension G with finitely generated commutator subgroup G but has a finite index normal subgroup H with infinitely generated H.
