4 papers
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.…
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 famil…
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 BroÄiÄ and Shelukhin. We construct counterexamples in dimension four usin…
Semi-Local Exotic Lagrangian Tori in Dimension Four
Joé Brendel, Johannes Hauber, Joel Schmitz
We study exotic Lagrangian tori in dimension four. In certain Stein domains (which naturally appear in almost toric fibrations) we find families of monotone Lagrang…