Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 9, Number 1 (2009), 305-325.
Intersections and joins of free groups
Let and be subgroups of a free group of ranks and , 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 –manifolds.
We also prove the following particular case of the Hanna Neumann Conjecture, which has also been obtained by Louder. If has rank at least , then has rank no more than .
Algebr. Geom. Topol., Volume 9, Number 1 (2009), 305-325.
Received: 31 January 2008
Revised: 18 August 2008
Accepted: 28 January 2009
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20E05: Free nonabelian groups
Secondary: 57M50: Geometric structures on low-dimensional manifolds
Kent, Richard Peabody. Intersections and joins of free groups. Algebr. Geom. Topol. 9 (2009), no. 1, 305--325. doi:10.2140/agt.2009.9.305. https://projecteuclid.org/euclid.agt/1513796967