Vol. 301, No. 1, 2019

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Loxodromics for the cyclic splitting complex and their centralizers

Radhika Gupta and Derrick Wigglesworth

Vol. 301 (2019), No. 1, 107–142
DOI: 10.2140/pjm.2019.301.107
Abstract

We show that an outer automorphism acts loxodromically on the cyclic splitting complex if and only if it has a filling lamination and no generic leaf of the lamination is carried by a vertex group of a cyclic splitting. This is the analog for the cyclic splitting complex of Handel–Mosher’s theorem on loxodromics for the free splitting complex. We also show that such outer automorphisms have virtually cyclic centralizers.

Keywords
curve graph, loxodromic, free splitting complex, automorphism groups, free factor complex, cyclic splitting complex, free groups
Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 20F28, 20E05, 57M07
Milestones
Received: 3 February 2018
Revised: 31 August 2018
Accepted: 15 November 2018
Published: 16 September 2019
Authors
Radhika Gupta
Department of Mathematics
Technion – Israel Institute of Technology
Haifa
Israel
Derrick Wigglesworth
Department of Mathematical Sciences
University of Arkansas
Fayetteville, AR
United States