Duke Mathematical Journal

On train-track splitting sequences

Howard Masur, Lee Mosher, and Saul Schleimer

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We present a structure theorem for the subsurface projections of train-track splitting sequences. For the proof we introduce induced tracks, efficient position, and wide curves. As a consequence of the structure theorem, we prove that train-track sliding and splitting sequences give quasi-geodesics in the train-track graph; this generalizes a result of Hamenstädt.

Article information

Duke Math. J. Volume 161, Number 9 (2012), 1613-1656.

First available in Project Euclid: 6 June 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M60: Group actions in low dimensions
Secondary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]


Masur, Howard; Mosher, Lee; Schleimer, Saul. On train-track splitting sequences. Duke Math. J. 161 (2012), no. 9, 1613--1656. doi:10.1215/00127094-1593344. http://projecteuclid.org/euclid.dmj/1338987165.

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