Packing Densities of Delzant and Semitoric Polygons

• Опубліковано в: : Symmetry, Integrability and Geometry: Methods and Applications
• Дата: 2023
• Автори: Du, Yu, Kosmacher, Gabriel, Liu, Yichen, Massman, Jeff, Palmer, Joseph, Thieme, Timothy, Wu, Jerry, Zhang, Zheyu
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут математики НАН України 2023
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/212050
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: Packing Densities of Delzant and Semitoric Polygons. Yu Du, Gabriel Kosmacher, Yichen Liu, Jeff Massman, Joseph Palmer, Timothy Thieme, Jerry Wu and Zheyu Zhang. SIGMA 19 (2023), 081, 42 pages

Exploiting the relationship between 4-dimensional toric and semitoric integrable systems with Delzant and semitoric polygons, respectively, we develop techniques to compute certain equivariant packing densities and equivariant capacities of these systems by working exclusively with the polygons. This expands on the results of Pelayo and Pelayo-Schmidt. We compute the densities of several important examples, and we also use our techniques to solve the equivariant semitoric perfect packing problem, i.e., we list all semitoric polygons for which the associated semitoric system admits an equivariant packing that fills all but a set of measure zero of the manifold. This paper also serves as a concise and accessible introduction to Delzant and semitoric polygons in dimension four.