Algebraic & Geometric Topology

Graphs of subgroups of free groups

Larsen Louder and D B McReynolds

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Abstract

We construct an efficient model for graphs of finitely generated subgroups of free groups. Using this we give a very short proof of Dicks’s reformulation of the strengthened Hanna Neumann Conjecture as the Amalgamated Graph Conjecture. In addition, we answer a question of Culler and Shalen on ranks of intersections in free groups. The latter has also been done independently by R P Kent IV.

Article information

Source
Algebr. Geom. Topol., Volume 9, Number 1 (2009), 327-335.

Dates
Received: 27 August 2008
Revised: 25 January 2009
Accepted: 28 January 2009
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796968

Digital Object Identifier
doi:10.2140/agt.2009.9.327

Mathematical Reviews number (MathSciNet)
MR2482080

Zentralblatt MATH identifier
1185.20026

Subjects
Primary: 20E05: Free nonabelian groups

Keywords
folding free groups Hanna Neumann conjecture

Citation

Louder, Larsen; McReynolds, D B. Graphs of subgroups of free groups. Algebr. Geom. Topol. 9 (2009), no. 1, 327--335. doi:10.2140/agt.2009.9.327. https://projecteuclid.org/euclid.agt/1513796968


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References

  • M Culler, P B Shalen, Four-free groups and hyperbolic geometry
  • W Dicks, Equivalence of the strengthened Hanna Neumann conjecture and the amalgamated graph conjecture, Invent. Math. 117 (1994) 373–389
  • R P Kent IV, Intersections and joins of free groups, Algebr. Geom. Topol. 9 (2009) 305–325
  • L Louder, Krull dimension for limit groups III: Scott complexity and adjoining roots to finitely generated groups
  • J R Stallings, Topology of finite graphs, Invent. Math. 71 (1983) 551–565