LIMIT SETS OF UNFOLDING PATHS IN OUTER SPACE

We construct an unfolding path in Outer space which does not converge in the boundary, and instead it accumulates on the entire 1-simplex of projectivized length measures on a nongeometric arational ${\mathbb R}$ -tree T. We also show that T admits exactly two dual ergodic projective currents. This...

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Bibliographic Details
Published in:Journal of the Institute of Mathematics of Jussieu 2024-09, Vol.23 (5), p.2365-2403
Main Authors: Bestvina, Mladen, Gupta, Radhika, Tao, Jing
Format: Article
Language:English
Subjects:
Construction
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Summary:We construct an unfolding path in Outer space which does not converge in the boundary, and instead it accumulates on the entire 1-simplex of projectivized length measures on a nongeometric arational ${\mathbb R}$ -tree T. We also show that T admits exactly two dual ergodic projective currents. This is the first nongeometric example of an arational tree that is neither uniquely ergodic nor uniquely ergometric.
ISSN:1474-7480
1475-3030
DOI:10.1017/S1474748023000488