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Loxodromics for the
cyclic splitting complex and their centralizers
Radhika Gupta and Derrick Wigglesworth |
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Vol. 301 (2019), No. 1, 107–142
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Abstract |
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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. |
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Keywords
curve graph, loxodromic, free splitting complex,
automorphism groups, free factor complex, cyclic splitting
complex, free groups
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Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 20F28, 20E05, 57M07
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Milestones
Received: 3 February 2018
Revised: 31 August 2018
Accepted: 15 November 2018
Published: 16 September 2019
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Authors |
| Radhika Gupta | |
| Department of Mathematics Technion – Israel Institute of Technology Haifa Israel |
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| Derrick Wigglesworth | |
| Department of Mathematical
Sciences University of Arkansas Fayetteville, AR United States |
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