A counterexample to Lagrangian Poincar\'e recurrence

TL;DR

This paper presents a counterexample to a longstanding conjecture in symplectic geometry, specifically the Lagrangian Poincaré recurrence, in all dimensions six and higher, challenging previous assumptions about recurrence properties.

Contribution

The authors construct the first known counterexample to the Lagrangian Poincaré recurrence conjecture in dimensions six and above, disproving the conjecture in these cases.

Findings

Counterexample exists in all dimensions ≥6

Disproves the Lagrangian Poincaré recurrence conjecture

Impacts understanding of recurrence in symplectic geometry

Abstract

We provide a counterexample to the Lagrangian Poincar\'e recurrence conjecture of Ginzburg and Viterbo in all dimensions $6$ and greater.