Submission date: 5 August 2016

Abstract:

We show that in general for a given group the structure of a maximal hyperbolic tower over a free group is not canonical: We construct examples of groups having hyperbolic tower structures over free subgroups which have arbitrarily large ratios between their ranks. These groups have the same first order theory as non-abelian free groups and we use them to study the weight of types in this theory.

Mathematics Subject Classification: 03Cxx, 20F65

Keywords and phrases: free groups; hyperbolic towers; geometric group theory; Bass-Serre theory; covering spaces; Whitehead graphs; surface groups; weight; stability theory.

Full text arXiv 1608.01845: pdf, ps.