Memoirs of the American Mathematical Society 2011; 153 pp; softcover Volume: 212 ISBN10: 0821852582 ISBN13: 9780821852583 List Price: US$77 Individual Members: US$46.20 Institutional Members: US$61.60 Order Code: MEMO/212/999
 Using an analogue of MakaninRazborov diagrams, the authors give an effective description of the solution set of systems of equations over a partially commutative group (rightangled Artin group) \(\mathbb{G}\). Equivalently, they give a parametrisation of \(\mathrm{Hom}(G, \mathbb{G})\), where \(G\) is a finitely generated group. Table of Contents  Introduction
 Preliminaries
 Reducing systems of equations over \(\mathbb{G}\) to constrained generalised equations over \(\mathbb{F}\)
 The process: Construction of the tree \(T\)
 Minimal solutions
 Periodic structures
 The finite tree \(T_0(\Omega)\) and minimal solutions
 From the coordinate group \(\mathbb{G}_{R(\Omega^*)}\) to proper quotients: The decomposition tree \(T_{\mathrm{dec}}\) and the extension tree \(T_{\mathrm{ext}}\)
 The solution tree \(T_{\mathrm{sol}}(\Omega)\) and the main theorem
 Bibliography
 Index
 Glossary of notation
