Nuez González, Javier de la: On expansions of non-abelian free groups by cosets of a finite index subgroup. 2016
Inhalt
- Introduction
- Preliminaries
- Reminder: the free group
- A few words about first order logic
- Introducing our setting and some basic definitions
- Preorders
- Actions on trees
- R-trees
- Simplicial trees: Bass-Serre theory
- Operations on trees
- Trees and surfaces
- Simplicial trees and group automorphisms
- Grushko and JSJ decompositions
- Limits of trees and the shortening argument
- Limits of actions on real trees: the Bestvina Paulin method
- Definitions
- Compactness, rescaling and apriori basepoints
- Limit actions of increasingly acylindrical sequences of actions
- Limit actions induced by a sequence of homomorphisms
- Trees of actions
- Rips' decomposition
- The shortening argument
- Makanin-Razborov diagrams
- Basic notions
- The Makanin-Razborov procedure
- Strict -resolutions
- Well-separated -resolutions
- Taut -resolutions
- -Towers
- Definition
- Closures
- Completions
- -test sequences
- Existence of -test sequences
- Characterization of restricted -limit groups
- Merzlyakov-type theorems