Limits of Thompson's group F
by
Roland Zarzycki
University of Wroclaw

Denote by F the Thompson's group F with standard presentation: F=〈x₀, x₁|[x₀x₁^-1, x₀^-1x₁x₀], [x₀x₁^-1, x₀^-2x₁x₀²]〉 and fix a sequence { g_i } _{i ∈ N}, where g_i ∈ F for all i. Let G_i=〈x₀, x₁, x₂|[x₀x₁^-1, x₀^-1x₁x₀], [x₀x₁^-1, x₀^-2x₁x₀²], x^-1₂ g_i〉 be a sequence of isomorphic copies of F marked by three elements. We investigate the convergence of such sequences and possible limit groups constructed in this manner. It is easy to see, that at infinity we can get free and direct products of F with Z. We study free constructions involving F and Z which can be obtained by this procedure. In particular, we prove that no (centralized) HNN-extensions occur as F-limit group.

Date received: March 9, 2006