Diophantine geometry over groups I: Makanin-Razborov diagrams

By Z. Sela. 2001

317 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/92cd81757ad64bdf16853e50ccda565b57561c35

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Vincent Guirardel
2. Denis V. Osin
3. D. Groves
4. Alexei G. Myasnikov
5. Alessandro Sisto
6. Henry Wilton
7. Gilbert Levitt
8. Franccois Dahmani

In Mathematical Physics

1. Vincent Guirardel
2. Denis V. Osin
3. Alessandro Sisto
4. Alexei G. Myasnikov
5. Henry Wilton
6. D. Groves
7. Gilbert Levitt
8. Franccois Dahmani

Citations in the corpus

• Unification theorems in algebraic geometry (2008, background): “…G -groups) [2, 3, 34, 5, 6], in the algebraic geometry over groups as the coordinate groups of irreducible varieties over G [4, 24, 25, 26, 47], groups universally equivalent to G [40, 13, 34], limit groups of G in the Grigorchuk-Gromov’s metric [10], in the theory of equations in groups…”
• Diophantine geometry over groups VI: the elementary theory of a free group (2006, methodology): “By section 2 of [ Se1 ], since B is a freely-indecomposable hyperbolic limit group that is not isomorphic to a surface group, it admits a non-trivial abelian JSJ decomposition, and since B is hyperbolic, its abelian JSJ decomposition is a cyclic JSJ decomposition with no non-cyclic abelian vertex gr”
• The Borel Conjecture for hyperbolic and CAT(0)-groups (2009, methodology): “Thus the FarrellJones Conjecture in K- and L-theory holds for the only at present known counterexamples to the Baum-Connes Conjecture with coefficients.”
• Elementary theory of free non-abelian groups (2006, methodology): “While this paper was going through the refereeing and revision, another proof of the first theorem, due to Sela, appeared in a series of preprints [28–33].”
• Hall’s Theorem for Limit Groups (2006, background): “For the proofs of these assertions, see Lemmas 1.4, 2.1 and 2.3 of [ 20 ].”
• Diophantine geometry over groups VII: The elementary theory of a hyperbolic group (2009, methodology): “The same construction that appears in [18] applies to Γ-limit groups (where Γ is torsion-free hyperbolic).”
• Foliations for solving equations in groups: free, virtually free, and hyperbolic groups (2009, background): “V. Guirardel, ‘Approximations of stable actions on R-trees’, Comment.”
• On the finite presentation of subdirect products and the nature of residually free groups (2012, background): “By definition, ∃ -free groups have the same universal theory as a free group; they are now more commonly known as limit groups , a term coined by Sela [37].”