arXiv subjects
Publications and source records attributed to Aerim Si.
In this paper, we study the fiber connectivity of proper almost-toric systems $Φ$ on connected four-dimensional symplectic manifolds. Using Morse--Kirwan theory, we establish three sufficient conditions for fiber connectivity. These results generalize and extend the fiber connectivity results of Pelayo, Ratiu, and Vu Ngoc (2015) by relaxing some of their hypotheses.
Semitoric systems are a special type of 4-dimensional integrable system where one of the functions is the moment map of a Hamiltonian $S^1$-action. While their classification is well understood thanks to the work of Pelayo and V{ũ} Ng\d{o}c, relatively few explicit examples are known. Recently, Le Floch and Palmer introduced semitoric transition families in which a singular point transitions between elliptic-elliptic type and focus-focus type as the parameter varies. In this paper, we construct new semitoric transition families on pentagon spaces by interpolating two semitoric systems of toric type. More precisely, we exhibit semitoric transition families, each with at least one transition point, on pentagon spaces of different diffeotypes, all defined by the same explicit interpolation formula.