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arXiv · 1710.10478

Loxodromic elements in the cyclic splitting complex and their centralizers

Radhika Gupta·Derrick Wigglesworth
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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.

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Radhika Gupta, Derrick Wigglesworth. 2017-10-28. Loxodromic elements in the cyclic splitting complex and their centralizers. https://doi.org/10.2140/pjm.2019.301.107

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