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2012 Spectral rigidity of automorphic orbits in free groups
Mathieu Carette, Stefano Francaviglia, Ilya Kapovich, Armando Martino
Algebr. Geom. Topol. 12(3): 1457-1486 (2012). DOI: 10.2140/agt.2012.12.1457


It is well-known that a point T cvN in the (unprojectivized) Culler–Vogtmann Outer space cvN is uniquely determined by its translation length function T:FN. A subset S of a free group FN is called spectrally rigid if, whenever T,T cvN are such that gT=gT for every gS then T=T in cvN. By contrast to the similar questions for the Teichmüller space, it is known that for N2 there does not exist a finite spectrally rigid subset of FN.

In this paper we prove that for N3 if H Aut(FN) is a subgroup that projects to a nontrivial normal subgroup in Out(FN) then the H–orbit of an arbitrary nontrivial element gFN is spectrally rigid. We also establish a similar statement for F2=F(a,b), provided that gF2 is not conjugate to a power of [a,b].


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Mathieu Carette. Stefano Francaviglia. Ilya Kapovich. Armando Martino. "Spectral rigidity of automorphic orbits in free groups." Algebr. Geom. Topol. 12 (3) 1457 - 1486, 2012.


Received: 3 June 2011; Revised: 19 April 2012; Accepted: 2 May 2012; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1261.20040
MathSciNet: MR2966693
Digital Object Identifier: 10.2140/agt.2012.12.1457

Primary: 20E08, 20F65
Secondary: 53C24, 57M07, 57M50

Rights: Copyright © 2012 Mathematical Sciences Publishers


Vol.12 • No. 3 • 2012
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