Algebraic Geometry over Groups

By G. Baumslag, A. Miasnikov, Vladimir Nikanorovich Remeslennikov. 2000

180 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2d401da9cccb1b24f02c9ee66eba735bf2050d00

How researchers see this paper

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

In Algebra and Number Theory

1. Alexei G. Myasnikov
2. Alan W. Reid
3. Martin R. Bridson
4. Denis V. Osin
5. Vincent Guirardel
6. Dikran Dikranjan
7. Christophe Champetier
8. Marston D. E. Conder

In Geometry and Topology

1. Michael Hull
2. Denis V. Osin
3. Alexei G. Myasnikov
4. Vincent Guirardel
5. Martin R. Bridson
6. Olga Kharlampovich
7. Charles F. Miller
8. James Howie

In Mathematical Physics

1. Michael Hull
2. Denis V. Osin
3. Alexei G. Myasnikov
4. Vincent Guirardel
5. Martin R. Bridson
6. Olga Kharlampovich
7. Charles F. Miller
8. James Howie

Citations in the corpus

• On the finite presentation of subdirect products and the nature of residually free groups (2012, background): “The embedding theorem from [3] tells us that S embeds into the direct product of a finite collection of limit groups.”
• Effective JSJ Decompositions (2004, background): “We refer to [4] for a general discussion on G-groups.”
• Algebras with the same (algebraic) geometry (2002, background): “If algebras H1 and H2 are geometrically equivalent, then the categories CΘ(H1) and CΘ(H2) coincide, while categories KΘ(H1) and KΘ(H2) are isomorphic.”
• Transitivity degrees of countable groups and acylindrical hyperbolicity (2015, background): “Groups universally equivalent to G as G-groups are exactly the coordinate groups of irreducible algebraic varieties over G [7].”
• The Markov–Zariski topology of an abelian group (2010, background): “6 to the groups E1 = G[2] and E2 = G[3], we conclude that E1 and E2 are irreducible (and hence, connected) ZG-closed subsets of G.”
• Determining Fuchsian groups by their finite quotients (2014, background): “Every finitely-generated residually free group Γ is a subgroup of a direct product of finitely many limit groups [8].”
• Limit groups as limits of free groups: compactifying the set of free groups. (2004, background): “These groups appeared to coincide with the long-studied class of finitely generated fully residually free groups (definition 2.5, see [Bau67], [Bau62], [KM98a, KM98b], see [ BMR00 ] and [Chi95] and references).”