Year: 2025
Type: article
Abstract: For a surface S of sufficient complexity, Dehn twists act elliptically on the arc, curve, or 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 $$\mathcal {A}(S,p)$$ A ( S , p ) for any surface S with an isolated puncture p admitting a shift map. Therefore, shift maps are not type-preserving.
Source: Geometriae Dedicata
Authors: Carolyn Abbott, Nicholas Miller, Priyam Patel
Institutions: Brandeis University, University of Oklahoma, University of Utah
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,090
Awards: Hyperbolic Manifolds, Geodesic Submanifolds, and Rigidity for Rank-1 Lattices, G2840664565, CAREER: The Algebra, Geometry, and Topology of Infinite Surfaces, CAREER: Large scale geometry and negative curvature, G6671297155, Rigidity Theorems for Lattices, Group Actions on Hyperbolic Spaces, G7825550202, G813328539, Hyperbolic Manifolds, Geodesic Submanifolds, and Rigidity for Rank-1 Lattices
OpenAlex ID: W4414822450