Snake Graphs from Triangulated Orbifolds

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2020
• Main Authors: Banaian, Esther, Kelley, Elizabeth
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211081
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Snake Graphs from Triangulated Orbifolds. Esther Banaian and Elizabeth Kelley. SIGMA 16 (2020), 138, 50 pages

We give an explicit combinatorial formula for the Laurent expansion of any arc or closed curve on an unpunctured triangulated orbifold. We do this by extending the snake graph construction of Musiker, Schiffler, and Williams to unpunctured orbifolds. In the case of an ordinary arc, this gives a comb...