3 papers
math.SG2025
More counterexamples to Lagrangian Poincaré recurrence in dimension four
Joel Schmitz
In earlier work, we constructed counterexamples to Lagrangian Poincaré recurrence for many toric symplectic four manifolds. Here we provide a few more examples extending the family…
math.SG2025
Nodal Tangles
Joel Schmitz
We study piecewise linear knot diagrams in the base of almost toric fibrations of symplectic four-manifolds. These diagrams translate to deformations of the almost toric fibration.…
math.SG2024
A counterexample to Lagrangian Poincaré recurrence in dimension four
Joel Schmitz
Counterexamples to Lagrangian Poincaré recurrence were recently found in dimensions greater than six by Broćić and Shelukhin. We construct counterexamples in dimension four using a…