47 citations · 146 across the 18 of their papers we have counts for
20 papers
Non-decomposable Lagrangian endoconcordances and Khovanov homology
Roman Golovko
In this note, we construct non-decomposable Lagrangian endoconcordances of Legendrian knots. We prove that for any positive integer k, there exist a (stabilised) Legendrian knot an…
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…
On non-geometric augmentations in high dimensions
Roman Golovko
In this note we construct augmentations of Chekanov-Eliashberg algebras of certain high dimensional Legendrian submanifolds that are not induced by exact Lagrangian fillings. The o…
On torsion in linearized Legendrian contact homology
Roman Golovko
In this short note we discuss certain examples of Legendrian submanifolds, whose linearized Legendrian contact (co)homology groups over integers have non-vanishing algebraic torsio…
A note on infinite number of exact Lagrangian fillings for spherical spuns
Roman Golovko
In this short note we discuss high-dimensional examples of Legendrian submanifolds of the standard contact Euclidean space with an infinite number of exact Lagrangian fillings up t…
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…
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…
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…
A Novikov fundamental group
Jean-François Barraud, Agnès Gadbled, Hông Vân Lê +1
Given a -cohomology class on a closed manifold , we define a Novikov fundamental group associated to , generalizing the usual fundamental group in the same spirit as N…
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…
Floer theory for Lagrangian cobordisms
Baptiste Chantraine, Georgios Dimitroglou Rizell, Paolo Ghiggini +1
In this article we define intersection Floer homology for exact Lagrangian cobordisms between Legendrian submanifolds in the contactisation of a Liouville manifold, provided that t…
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…
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…
Polyfolds: A First and Second Look
Oliver Fabert, Joel W. Fish, Roman Golovko +1
Polyfold theory was developed by Hofer-Wysocki-Zehnder by finding commonalities in the analytic framework for a variety of geometric elliptic PDEs, in particular moduli spaces of p…
A note on Lagrangian cobordisms between Legendrian submanifolds of R^{2n+1}
Roman Golovko
We study the relation of an embedded Lagrangian cobordism between two closed, orientable Legendrian submanifolds of R^{2n+1}. More precisely, we investigate the behavior of the Thu…
The cylindrical contact homology of universally tight sutured contact solid tori
Roman Golovko
We calculate the sutured version of cylindrical contact homology of a sutured contact solid torus , where consists of parallel sutures of arbitrary s…
The embedded contact homology of sutured solid tori
Roman Golovko
We calculate the relative versions of embedded contact homology, contact homology and cylindrical contact homology of the sutured solid torus , where consist…