Geometry & Topology
- Geom. Topol.
- Volume 13, Number 3 (2009), 1805-1833.
Geometric intersection number and analogues of the curve complex for free groups
For the free group of finite rank we construct a canonical Bonahon-type, continuous and –invariant geometric intersection form
Here is the closure of unprojectivized Culler–Vogtmann Outer space in the equivariant Gromov–Hausdorff convergence topology (or, equivalently, in the length function topology). It is known that consists of all very small minimal isometric actions of on –trees. The projectivization of provides a free group analogue of Thurston’s compactification of Teichmüller space.
As an application, using the intersection graph determined by the intersection form, we show that several natural analogues of the curve complex in the free group context have infinite diameter.
Geom. Topol., Volume 13, Number 3 (2009), 1805-1833.
Received: 26 August 2008
Accepted: 6 November 2008
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Secondary: 57M99: None of the above, but in this section 37B99: None of the above, but in this section 37D99: None of the above, but in this section
Kapovich, Ilya; Lustig, Martin. Geometric intersection number and analogues of the curve complex for free groups. Geom. Topol. 13 (2009), no. 3, 1805--1833. doi:10.2140/gt.2009.13.1805. https://projecteuclid.org/euclid.gt/1513800259