Geodesic currents and length compactness for automorphisms of free groups

Stefano Francaviglia

doi:10.1090/S0002-9947-08-04420-6

Geodesic currents and length compactness for automorphisms of free groups

Stefano Francaviglia

Research output: Contribution to journal › Article › Research › peer-review

15 Citations (Scopus)

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. © 2008 American Mathematical Society.

Original language	English
Pages (from-to)	161-176
Journal	Transactions of the American Mathematical Society
Volume	361
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9947-08-04420-6
Publication status	Published - 1 Jan 2009

Keywords

Automorphisms
Free groups
Geodesic currents

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10.1090/S0002-9947-08-04420-6

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AB - 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. © 2008 American Mathematical Society.

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KW - Free groups

KW - Geodesic currents

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DO - 10.1090/S0002-9947-08-04420-6

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JO - Transactions of the American Mathematical Society

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SN - 0002-9947

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Geodesic currents and length compactness for automorphisms of free groups

Abstract

Keywords

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