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Geodesic currents and length compactness for automorphisms of free groups
Author(s):
Stefano
Francaviglia
Journal:
Trans. Amer. Math. Soc.
361
(2009),
161-176.
MSC (2000):
Primary 20F65
Posted:
August 13, 2008
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Abstract:
We prove a compactness theorem for automorphisms of free groups. Namely, we show that the set of automorphisms keeping the length of the uniform current bounded is compact (up to conjugation). This implies that the spectrum of the length of the images of the uniform current is discrete, proving a conjecture of I. Kapovich.
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Additional Information:
Stefano
Francaviglia
Affiliation:
Departament de Matemàtiques, Edifici C, Universitat Autònoma, 08193 Bellaterra (Barcelona) Spain
Email:
s.francaviglia@sns.it
DOI:
10.1090/S0002-9947-08-04420-6
PII:
S 0002-9947(08)04420-6
Keywords:
Automorphisms,
free groups,
geodesic currents
Received by editor(s):
May 22, 2006
Received by editor(s) in revised form:
October 25, 2006
Posted:
August 13, 2008
Additional Notes:
The author was supported by a Marie Curie Intra European Fellowship.
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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