Geodesic
Graphs of subgroups of free groups
Louder, Larsen1 ; McReynolds, D B2
1Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1043, USA
2Department of Mathematics, University of Chicago, Chicago, IL 60637, USA
Algebraic and Geometric Topology, Tome 9 (2009) no. 1, pp. 327-335
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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.

DOI : 10.2140/agt.2009.9.327
Keywords: folding, free groups, Hanna Neumann conjecture

Louder, Larsen  1   ; McReynolds, D B  2

1 Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1043, USA
2 Department of Mathematics, University of Chicago, Chicago, IL 60637, USA 
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Louder, Larsen; McReynolds, D B. Graphs of subgroups of free groups. Algebraic and Geometric Topology, Tome 9 (2009) no. 1, pp. 327-335. doi: 10.2140/agt.2009.9.327

[1] M Culler, P B Shalen, Four-free groups and hyperbolic geometry

[2] W Dicks, Equivalence of the strengthened Hanna Neumann conjecture and the amalgamated graph conjecture, Invent. Math. 117 (1994) 373

[3] R P Kent Iv, Intersections and joins of free groups, Algebr. Geom. Topol. 9 (2009) 305

[4] L Louder, Krull dimension for limit groups III: Scott complexity and adjoining roots to finitely generated groups

[5] J R Stallings, Topology of finite graphs, Invent. Math. 71 (1983) 551

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