Subgroups of quasi-HNN groups

Subgroups of Quasi-hnn Groups

Perfect Subgroups of Hnn Extensions

This note includes supporting material for Guilbault’s one-hour talk summarized elsewhere in these proceedings. We supply the group theory necessary to argue that Guilbault’s tame ends cannot be pseudocollared. In particular, we show that certain groups (the interated Baumslag-Solitar groups) cannot have any non-trivial perfect subgroups. The absence of non-trivial perfect subgroups, in turn, e...

Quasi-isometrically Embedded Subgroups of Braid and Diffeomorphism Groups

We show that a large class of right-angled Artin groups (in particular, those with planar complementary defining graph) can be embedded quasi-isometrically in pure braid groups and in the group Diff(D2, ∂D2, vol) of area preserving diffeomorphisms of the disk fixing the boundary (with respect to the L2-norm metric); this extends results of Benaim and Gambaudo who gave quasi-isometric embeddings...

Quasi-convex density and determining subgroups of compact abelian groups

For an abelian topological group G, let Ĝ denote the dual group of all continuous characters endowed with the compact open topology. Given a closed subset X of an infinite compact abelian group G such that w(X) < w(G), and an open neighbourhood U of 0 in T, we show that |{χ ∈ Ĝ : χ(X) ⊆ U}| = |Ĝ|. (Here, w(G) denotes the weight of G.) A subgroup D of G determines G if the map r : Ĝ → D̂ defined ...

A remark on the intersection of the conjugates of the base of quasi-HNN groups

Quasi-HNN groups can be characterized as a generalization of HNN groups. In this paper, we show that if G * is a quasi-HNN group of base G, then either any two conjugates of G are identical or their intersection is contained in a conjugate of an associated subgroup of G.