55 citations · 212 across the 26 of their papers we have counts for
28 papers
Representations of the Chekanov-Eliashberg algebra from closed exact Lagrangians I
Baptiste Chantraine, Georgios Dimitroglou Rizell, Paolo Ghiggini
This is the first of a series of two articles aiming at relating the compact Fukaya category of a Weinstein manifold to the derived category of finite dimensional representations o…
Rationally Convex Surfaces with hyperbolic complex tangencies
Georgios Dimitroglou Rizell, Mark G. Lawrence
We construct the first examples of rationally convex surfaces in the complex plane with hyperbolic complex tangencies. In fact, we give two very different types of rationally conve…
Construction of symplectic flexible links
Johan Björklund, Georgios Dimitroglou Rizell
We show that any smooth one-dimensional link in the real projective three-plane is the fixed-point locus of a smooth symplectic surface in the complex projective three-plane which…
On weakly exact Lagrangians in Liouville bi-fillings
Georgios Dimitroglou Rizell
Here we study several questions concerning Liouville domains that are diffeomorphic to cylinders, so called trivial bi-fillings, for which the Liouville skeleton moreover is smooth…
Instability of Legendrian knottedness, and non-regular Lagrangian concordances of knots
Georgios Dimitroglou Rizell, Roman Golovko
We show that the family of smoothly non-isotopic Legendrian pretzel knots from the work of Cornwell-Ng-Sivek that all have the same Legendrian invariants as the standard unknot hav…
Lagrangian Surplusection Phenomena
Georgios Dimitroglou Rizell, Jonathan David Evans
Suppose you have a family of Lagrangian submanifolds and an auxiliary Lagrangian . Suppose that intersects some of the more than the minimal number of times. Can…
-limits of Legendrian knots and contact non-squeezing
Georgios Dimitroglou Rizell, Michael G. Sullivan
Take a sequence of contactomorphisms of a contact three-manifold that -converges to a homeomorphism. If the images of a Legendrian knot limit to a smooth knot under this seque…
Linking of Lagrangian Tori and Embedding Obstructions in Symplectic 4-Manifolds
Laurent Côté, Georgios Dimitroglou Rizell
We classify weakly exact, rational Lagrangian tori in up to Hamiltonian isotopy. This result is related to the classification theory of closed…
On Legendrian products and twist spuns
Georgios Dimitroglou Rizell, Roman Golovko
The Legendrian product of two Legendrian knots, as defined by Lambert-Cole, is a Legendrian torus. We show that this Legendrian torus is a twist spun whenever one of the Legendrian…
Bulky Hamiltonian isotopies of Lagrangian tori with applications
Georgios Dimitroglou Rizell
We exhibit monotone Lagrangian tori inside the standard symplectic four-dimensional unit ball that become Hamiltonian isotopic to the Clifford torus, i.e.~the standard product toru…
Legendrian submanifolds from Bohr-Sommerfeld covers of monotone Lagrangian tori
Georgios Dimitroglou Rizell, Roman Golovko
By a result due to Ziltener, there exist no closed embedded Bohr-Sommerfeld Lagrangians inside for the prequantisation bundle whose total space is the standard conta…
Refined disk potentials for immersed Lagrangian surfaces
Georgios Dimitroglou Rizell, Tobias Ekholm, Dmitry Tonkonog
We define a refined Gromov-Witten disk potential of self-transverse monotone immersed Lagrangian surfaces in a symplectic 4-manifold as an element in a capped version of the Chekan…
Geometric generation of the wrapped Fukaya category of Weinstein manifolds and sectors
Baptiste Chantraine, Georgios Dimitroglou Rizell, Paolo Ghiggini +1
We prove that the wrapped Fukaya category of any -dimensional Weinstein manifold (or, more generally, Weinstein sector) is generated by the unstable manifolds of the index…
The classification of Lagrangians nearby the Whitney immersion
Georgios Dimitroglou Rizell
The Whitney immersion is a Lagrangian sphere inside the four-dimensional symplectic vector space which has a single transverse double point of Whitney self-intersection number $+1.…
The number of Hamiltonian fixed points on symplectically aspherical manifolds
Georgios Dimitroglou Rizell, Roman Golovko
We show that a generic Hamiltonian diffeomorphism on a closed symplectic manifold which is symplectically aspherical has at least the stable Morse number of fixed points - this is…
Noncommutative augmentation categories
Baptiste Chantraine, Georgios Dimitroglou Rizell, Paolo Ghiggini +1
To a differential graded algebra with coefficients in a noncommutative algebra, by dualisation we associate an -category whose objects are augmentations. This generalises…
Nontriviality results for the characteristic algebra of a DGA
Georgios Dimitroglou Rizell
Assume that we are given a semifree noncommutative differential graded algebra (DGA for short) whose differential respects an action filtration. We show that the canonical unital a…
Uniqueness of extremal Lagrangian tori in the four-dimensional disc
Georgios Dimitroglou Rizell
The following interesting quantity was introduced by K. Cieliebak and K. Mohnke for a Lagrangian submanifold of a symplectic manifold: the minimal positive symplectic area of a…
The stable Morse number as a lower bound for the number of Reeb chords
Georgios Dimitroglou Rizell, Roman Golovko
Assume that we are given a closed chord-generic Legendrian submanifold of the contactisation of a Liouville manifold, where moreover admits an exa…
Floer homology and Lagrangian concordance
Baptiste Chantraine, Georgios Dimitroglou Rizell, Paolo Ghiggini +1
We derive constraints on Lagrangian concordances from Legendrian submanifolds of the standard contact sphere admitting exact Lagrangian fillings. More precisely, we show that such…
Estimating the number of Reeb chords using a linear representation of the characteristic algebra
Georgios Dimitroglou Rizell, Roman Golovko
Given a chord-generic horizontally displaceable Legendrian submanifold with the property that its characteristic algebra admits a finite-dimensional ma…
Exotic spheres and the topology of symplectomorphism groups
Georgios Dimitroglou Rizell, Jonathan David Evans
We show that, for certain families of diffeomorphisms of high-dimensional spheres, the commutator of the Dehn twist along the zero-section of with the fam…
On homological rigidity and flexibility of exact Lagrangian endocobordisms
Georgios Dimitroglou Rizell, Roman Golovko
We show that an exact Lagrangian cobordism from a Legendrian submanifold to itself satisfies $H_i(L;\mat…
Exact Lagrangian caps and non-uniruled Lagrangian submanifolds
Georgios Dimitroglou Rizell
We make the elementary observation that the Lagrangian submanifolds of , for each , constructed by Ekholm, Eliashberg, Murphy and Smith are non-uniruled and…