Shifts maps are not type-preserving
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2022
- DOI:
- 10.48550/arXiv.2212.09156
- arXiv:
- arXiv:2212.09156
- Bibcode:
- 2022arXiv221209156A
- Keywords:
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- Mathematics - Geometric Topology
- E-Print:
- 15 pages, 12 figures