20 citations · 71 across the 11 of their papers we have counts for
13 papers
Super-rigidity of certain skeleta using relative symplectic cohomology
Dmitry Tonkonog, Umut Varolgunes
This article uses relative symplectic cohomology, recently studied by the second author, to understand rigidity phenomena for compact subsets of symplectic manifolds. As an applica…
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…
Geometry of symplectic flux and Lagrangian torus fibrations
Egor Shelukhin, Dmitry Tonkonog, Renato Vianna
Symplectic flux measures the areas of cylinders swept in the process of a Lagrangian isotopy. We study flux via a numerical invariant of a Lagrangian submanifold that we define usi…
String topology with gravitational descendants, and periods of Landau-Ginzburg potentials
Dmitry Tonkonog
This paper introduces new operations on the string topology of a smooth manifold: gravitational descendants of its cotangent bundle, which are augmentations of the Chas-Sullivan $L…
From symplectic cohomology to Lagrangian enumerative geometry
Dmitry Tonkonog
We build a bridge between Floer theory on open symplectic manifolds and the enumerative geometry of holomorphic disks inside their Fano compactifications, by detecting elements in…
The wall-crossing formula and Lagrangian mutations
James Pascaleff, Dmitry Tonkonog
We prove a general form of the wall-crossing formula which relates the disk potentials of monotone Lagrangian submanifolds with their Floer-theoretic behavior away from a Donaldson…
Low-area Floer theory and non-displaceability
Dmitry Tonkonog, Renato Vianna
We introduce a new version of Floer theory of a non-monotone Lagrangian submanifold which only uses least area holomorphic disks with boundary on it. We use this theory to prove no…
The closed-open string map for -invariant Lagrangians
Dmitry Tonkonog
Given a monotone Lagrangian submanifold invariant under a loop of Hamiltonian diffeomorphisms, we compute a piece of the closed-open string map into the Hochschild cohomology of th…
Commuting symplectomorphisms and Dehn twists in divisors
Dmitry Tonkonog
Two commuting symplectomorphisms of a symplectic manifold give rise to actions on Floer cohomologies of each other. We prove the elliptic relation saying that the supertraces of th…
Good covers are algorithmically unrecognizable
Martin Tancer, Dmitry Tonkonog
A good cover in R^d is a collection of open contractible sets in R^d such that the intersection of any subcollection is either contractible or empty. Motivated by an analogy with c…
Embedding punctured n-manifolds in Euclidean (2n-1)-space
Dmitry Tonkonog
Let be a closed orientable connected -manifold, . We classify embeddings of the punctured manifold into up to isotopy. Our result in some sense ext…
Singularities of integrable Hamiltonian systems: a criterion for non-degeneracy, with an application to the Manakov top
Dmitry Tonkonog
Let (M,ω) be a symplectic 2n-manifold and h_1,...,h_n be functionally independent commuting functions on M. We present a geometric criterion for a singular point P\in M (i.e. such…
Embedding 3-manifolds with boundary into closed 3-manifolds
Dmitry Tonkonog
We prove that there is an algorithm which determines whether or not a given 2-polyhedron can be embedded into some integral homology 3-sphere. This is a corollary of the following…