Notes on Sela's work: Limit groups and Makanin-Razborov diagrams
Mladen Bestvina, Mark Feighn
TL;DR
This paper provides an alternative exposition to Sela's work on the Tarski problems, focusing on parametrizing homomorphisms from finitely generated groups to free groups, building on prior foundational work.
Contribution
It offers a new approach to understanding the structure of limit groups and Makanin-Razborov diagrams, expanding on Kharlampovich-Myasnikov and Sela's results.
Findings
Parametrization of Hom(G,F) for finitely generated G and free group F
Alternative approach to Sela's work on the Tarski problems
Foundation for future papers in the series
Abstract
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 Hom(G,F) where G is a finitely generated group and F is a non-abelian free group.
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