Algebraic & Geometric Topology

Graphs of subgroups of free groups

Larsen Louder and D B McReynolds

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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.

Article information

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20E05: Free nonabelian groups

folding free groups Hanna Neumann conjecture


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.

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