Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 12, Number 3 (2012), 1457-1486.
Spectral rigidity of automorphic orbits in free groups
It is well-known that a point in the (unprojectivized) Culler–Vogtmann Outer space is uniquely determined by its translation length function . A subset of a free group is called spectrally rigid if, whenever are such that for every then in . By contrast to the similar questions for the Teichmüller space, it is known that for there does not exist a finite spectrally rigid subset of .
In this paper we prove that for if is a subgroup that projects to a nontrivial normal subgroup in then the –orbit of an arbitrary nontrivial element is spectrally rigid. We also establish a similar statement for , provided that is not conjugate to a power of .
Algebr. Geom. Topol., Volume 12, Number 3 (2012), 1457-1486.
Received: 3 June 2011
Revised: 19 April 2012
Accepted: 2 May 2012
First available in Project Euclid: 19 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20E08: Groups acting on trees [See also 20F65] 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Secondary: 57M07: Topological methods in group theory 57M50: Geometric structures on low-dimensional manifolds 53C24: Rigidity results
Carette, Mathieu; Francaviglia, Stefano; Kapovich, Ilya; Martino, Armando. Spectral rigidity of automorphic orbits in free groups. Algebr. Geom. Topol. 12 (2012), no. 3, 1457--1486. doi:10.2140/agt.2012.12.1457. https://projecteuclid.org/euclid.agt/1513715405