Year: 2025
Type: article
Abstract: We show that for every curve on † n P , the curve obtained by resolving the kinks of in any order is uniquely determined, up to homotopy in † n P , by the 2-orbifold homotopy class of , in which the punctures are interpreted to be orbifold points of order 2. Our proof relies on an application of the diamond lemma.57K20; 13F60, 18B40 1. Introduction 3679 2. Background 3682 3. The (leafy) dual graph of a triangulation of signature zero 3685 4. Kinks of walks on graphs 3689 5. Kinks of curves via kinks of walks on graphs 3699 6. Equivalence of orbifold fundamental groupoids 3702 7. Main result: uniqueness of kink-free representative curves 3704
Source: Algebraic & Geometric Topology
Authors: Christof Geiss, Daniel Labardini-Fragoso
Institutions: Universidad Nacional Autónoma de México, University of Padua
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4414971552