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Shifts maps are not type-preserving
Preprint

Shifts maps are not type-preserving

Carolyn Abbott, Nicholas Miller and Priyam Patel
arXiv
12/18/2022

Abstract

Mathematics - Geometric Topology
For a surface $S$ of sufficient complexity, Dehn twists act elliptically on the arc, curve, and relative arc graph of $S$. We show that composing a Dehn twist with a shift map results in a loxodromic isometry of the relative arc graph $\mathcal{A}(S,p)$ for any surface $S$ with an isolated puncture $p$ admitting a shift map. Therefore, shift maps are not type-preserving.

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