Geodesic
Intersections and joins of free groups
Kent, Richard Peabody1
1Department of Mathematics, Brown University, Providence, RI 02912
Algebraic and Geometric Topology, Tome 9 (2009) no. 1, pp. 305-325
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Let H and K be subgroups of a free group of ranks h and k ≥ h, respectively. We prove the following strong form of Burns’ inequality:

A corollary of this, also obtained by L Louder and D B McReynolds, has been used by M Culler and P Shalen to obtain information regarding the volumes of hyperbolic 3–manifolds.

We also prove the following particular case of the Hanna Neumann Conjecture, which has also been obtained by Louder. If H ∨ K has rank at least (h + k + 1)∕2, then H ∩ K has rank no more than (h − 1)(k − 1) + 1.

DOI : 10.2140/agt.2009.9.305
Keywords: free group, rank, intersection, join, Hanna Neumann Conjecture

Kent, Richard Peabody  1

1 Department of Mathematics, Brown University, Providence, RI 02912 
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Kent, Richard Peabody. Intersections and joins of free groups. Algebraic and Geometric Topology, Tome 9 (2009) no. 1, pp. 305-325. doi: 10.2140/agt.2009.9.305

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