Volume 12, issue 3 (2012)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Spectral rigidity of automorphic orbits in free groups

Mathieu Carette, Stefano Francaviglia, Ilya Kapovich and Armando Martino

Algebraic & Geometric Topology 12 (2012) 1457–1486
Abstract

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 g S then T = T in cvN. By contrast to the similar questions for the Teichmüller space, it is known that for N 2 there does not exist a finite spectrally rigid subset of FN.

In this paper we prove that for N 3 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 g FN is spectrally rigid. We also establish a similar statement for F2 = F(a,b), provided that g F2 is not conjugate to a power of [a,b].

Keywords
marked length spectrum rigidity, free groups, Outer space
Mathematical Subject Classification 2010
Primary: 20E08, 20F65
Secondary: 57M07, 57M50, 53C24
References
Publication
Received: 3 June 2011
Revised: 19 April 2012
Accepted: 2 May 2012
Published: 10 July 2012
Authors
Mathieu Carette
SST/IRMP
Chemin du Cyclotron 2
bte L7.01.01
1348 Louvain-la-Neuve
Belgium
Stefano Francaviglia
Dipartimento di Matematica of the University of Bologna
Piazza di Porta S. Donato 5
40126 Bologna
Italy
Ilya Kapovich
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 West Green Street
Urbana IL 61801
USA
Armando Martino
School of Mathematics
University of Southampton
Highfield
Southampton
SO17 1BJ
United Kingdom