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math.SG2020
Families of Legendrians and Lagrangians with unbounded spectral norm
Georgios Dimitroglou Rizell
Viterbo has conjectured that any Lagrangian in the unit co-disc bundle of a torus which is Hamiltonian isotopic to the zero-section satisfies a uniform bound on its spectral norm;…
math.SG2020
Symplectic Rigidity of Fibers in Cotangent Bundles of Open Riemann Surfaces
Laurent Côté, Georgios Dimitroglou Rizell
We study symplectic rigidity phenomena for fibers in cotangent bundles of Riemann surfaces. Our main result can be seen as a generalization to open Riemann surfaces of arbitrary ge…
math.SG2018
The persistence of the Chekanov-Eliashberg algebra
Georgios Dimitroglou Rizell, Michael G. Sullivan
We apply the barcodes of persistent homology theory to the Chekanov-Eliashberg algebra of a Legendrian submanifold to deduce displacement energy bounds for arbitrary Legendrians. W…