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RELATIVE TWISTING IN OUTER SPACE

MATT CLAY

Department of Mathematics, Allegheny College, Meadville, PA 16335, USA

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and

ALEXANDRA PETTET

Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada

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https://doi.org/10.1142/S1793525312500100Cited by:6 (Source: Crossref)

Abstract

Subsurface projection is indispensable to studying the geometry of the mapping class group and the curve complex of a surface. When the subsurface is an annulus, this projection is sometimes called relative twisting. We give two alternate versions of relative twisting for the outer automorphism group of a free group. We use this to describe sufficient conditions for when a folding path enters the thin part of Culler–Vogtmann's Outer space. As an application of our condition, we produce a sequence of fully irreducible outer automorphisms whose axes in Outer space travel through graphs with arbitrarily short cycles; we also describe the asymptotic behavior of their translation lengths.

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