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 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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