Publication
Title
Packing densities of Delzant and semitoric polygons
Author
Abstract
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 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 which 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.
Language
English
Source (journal)
Symmetry, Integrability and Geometry: Methods and Applications
Publication
2023
ISSN
1815-0659
DOI
10.3842/SIGMA.2023.081
Volume/pages
19 (2023) , p. 1-42
Article Reference
081
ISI
001122880600001
Full text (Publisher's DOI)
Full text (open access)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identifier
Creation 09.01.2024
Last edited 11.01.2024
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