Bestvina, Mladen; Feighn, Mark Notes on Sela’s work: limit groups and Makanin-Razborov diagrams. (English) Zbl 1213.20039 Bridson, Martin R. (ed.) et al., Geometric and cohomological methods in group theory. Papers from the London Mathematical Society symposium on geometry and cohomology in group theory, Durham, UK, July 2003. Cambridge: Cambridge University Press (ISBN 978-0-521-75724-9/pbk). London Mathematical Society Lecture Note Series 358, 1-29 (2009). Summary: This is the first in a planned series of papers giving an alternate approach to Zlil Sela’s work on the Tarski problems. The present paper is an exposition of work of Kharlampovich-Myasnikov and Sela giving a parametrization of \(\operatorname{Hom}(G,F)\) where \(G\) is a finitely generated group and \(F\) is a non-Abelian free group.For the entire collection see [Zbl 1197.20001]. Cited in 1 ReviewCited in 23 Documents MSC: 20F65 Geometric group theory 20F70 Algebraic geometry over groups; equations over groups 20E05 Free nonabelian groups 20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) 03B25 Decidability of theories and sets of sentences 20E26 Residual properties and generalizations; residually finite groups 20E36 Automorphisms of infinite groups Keywords:limit groups; free groups; equations over groups; Diophantine geometry over groups; Makanin-Razborov diagrams; JSJ-decompositions; finitely generated groups; residually free groups PDFBibTeX XMLCite \textit{M. Bestvina} and \textit{M. Feighn}, Lond. Math. Soc. Lect. Note Ser. 358, 1--29 (2009; Zbl 1213.20039) Full Text: arXiv