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Packing Densities of Delzant and Semitoric Polygons
Yu Dua, Gabriel Kosmachera, Yichen Liua, Jeff Massmana, Joseph Palmerab, Timothy Thiemea, Jerry Wua, Zheyu Zhanga a Department of Mathematics, University of Illinois at Urbana-Champaign,
Urbana, Illinois, USA
b Department of Mathematics, University of Antwerp, Antwerp, Belgium
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.
Keywords:
equivariant packing, equivariant symplectic capacities, semitoric integrable systems, semitoric polygons, integrable systems.
Received: November 22, 2022; in final form October 20, 2023; Published online October 29, 2023
Citation:
Yu Du, Gabriel Kosmacher, Yichen Liu, Jeff Massman, Joseph Palmer, Timothy Thieme, Jerry Wu, Zheyu Zhang, “Packing Densities of Delzant and Semitoric Polygons”, SIGMA, 19 (2023), 081, 42 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1976 https://www.mathnet.ru/eng/sigma/v19/p81
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Abstract page: | 27 | Full-text PDF : | 3 | References: | 10 |
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