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