arXiv research

Study on Legendrian knots and their non-orientable Lagrangian fillings.

The paper proves finiteness of cosmetic fillings on a specific type of 3-manifold.

Proves upper bound on systolic ratio for circle fillings.

Paper finds minimal number of curves in surface systems.

Affirmative proof that rank 3 3-manifolds have filling links.

We characterize the closed, oriented, Seifert fibered 3-manifolds which are oriented boundaries of Stein manifolds. We also show that for this class of 3-manifolds the existence of Stein fillings is equivalent to the existence of symplectic fillings.

Inspired by Gromov's work on 'Metric inequalities with scalar curvature' we establish band width inequalities for Riemannian bands of the form $(V=M\times[0,1],g)$, where $M^{n-1}$ is a closed manifold. We introduce a new class of orientable manifolds we call filling enlargeable and prove: If $M$ is filling enlargeable…

New augmentations of twist knots found that can't be filled.

The study examines dynamics on SU(2)-representation varieties for surfaces and non-orientable surfaces.

Gromov's universal filling inequalities relate the filling radius and the filling volume of a Riemannian manifold to its volume. The main result of the present article is that in dimensions at least three the optimal constants in the filling inequalities depend only on dimension and orientability, not on the manifold i…

We give a complete proof of Thurston's celebrated hyperbolic Dehn filling theorem, following the ideal triangulation approach of Thurston and Neumann-Zagier. We avoid to assume that a genuine ideal triangulation always exists, using only a partially flat one, obtained by subdividing an Epstein-Penner decomposition. Thi…

A conjecture due to Gompf asserts that no nontrivial Brieskorn homology sphere admits a pseudoconvex embedding in ${\mathbb C}^2$, with either orientation. A related question asks whether every compact contractible 4-manifold admits the structure of a Stein domain. We verify Gompf's conjecture, with one orientation, fo…

The paper proves left-orderability for certain Dehn fillings of pseudo-Anosov mapping tori.

We show that there are at most finitely many one cusped orientable hyperbolic 3-manifolds which have more than eight non-hyperbolic Dehn fillings. Moreover, we show that determining these finitely many manifolds is decidable.

This paper classifies symplectic and Stein fillings of contact 3-manifolds with spinal open book decompositions.

Census of 10-tetrahedra hyperbolic 3-manifolds with 150,730 new examples.

We characterize which Legendrian $4$-plat knots in the standard contact $3$-space have exact orientable Lagrangian fillings. As a corollary, we show that the underlying smooth knot types of fillable Legendrian $4$-plats are positive.

The paper connects Legendrian links to cluster theory and exact Lagrangian fillings.

Profinite rigidity of certain 3-manifolds detected through Dehn fillings.

The study confirms the non-existence of rational homology ball symplectic fillings for certain Brieskorn spheres.

In this paper we investigate the distances between Dehn fillings on a hyperbolic 3-manifold that yield 3-manifolds containing essential small surfaces including non-orientable surfaces. Especially we study the situations where one filling creates an essential sphere or projective plane, and the other creates an essenti…

Estimates the number of closed curves on surfaces with power-saving error terms.

In order to obtain a closed orientable convex projective four-manifold with small positive Euler characteristic, we build an explicit example of convex projective Dehn filling of a cusped hyperbolic four-manifold through a continuous path of projective cone-manifolds.

The study shows how to create co-orientable taut foliations in specific Dehn fillings.

Study uses Newton polytopes to distinguish Lagrangian fillings of Legendrian submanifolds.

The paper constructs minimal coherent filling pairs on surfaces.

Let $M$ be an irreducible, compact, connected, orientable 3-manifold whose boundary is a torus. We show that if $M$ is hyperbolic, then it admits at most six finite/cyclic fillings of maximal distance 5. Further, the distance of a finite/cyclic filling to a cyclic filling is at most 2. If $M$ has a non-boundary-paralle…

The taut polynomial equals a twisted Alexander polynomial.

Study filling links in 3-manifolds to understand their topological properties.

Integral filling volume of mapping tori grows sublinearly with complexity.

A filling Dehn sphere $Σ$ in a closed 3-manifold $M$ is a sphere transversely immersed in $M$ that defines a cell decomposition of $M$. Every closed 3-manifold has a filling Dehn sphere. The Montesinos complexity of a $3$-manifold $M$ is defined as the minimal number of triple points among all the filling Dehn spheres …

An oriented three-manifold with torus boundary admits either no L-space Dehn filling, a unique L-space filling, or an interval of L-space fillings. In the latter case, which we call "Floer simple," we construct an invariant which computes the interval of L-space filling slopes from the Turaev torsion and a given slope …

The abstract discusses applications of Menke's JSJ decomposition to symplectic fillings of various 3-manifolds.

Corrects classification of Seifert fibrations for lens spaces with non-orientable bases.

Maximizes filling systems on surfaces with given boundary components.

New links in 3-manifolds have large systole.

The article finds conditions for separating filling pairs on surfaces and constructs a Morse function.

A pair $(α, β)$ of simple closed geodesics on a closed and oriented hyperbolic surface $M_g$ of genus $g$ is called a filling pair if the complementary components of $α\cupβ$ in $M_g$ are simply connected. The length of a filling pair is defined to be the sum of their individual lengths. In \cite{Aou}, Aougab-Huang con…

Let C be the contact structure naturally induced on the lens space L(p,q) by the standard contact structure on the three--sphere. We obtain a complete classification of the symplectic fillings of (L(p,q),C) up to orientation-preserving diffeomorphisms. In view of our results, we formulate a conjecture on the diffeomorp…

Characterizes symplectic rational homology ball fillings of Seifert fibered spaces.

In this paper we give explicit, handle-by-handle constructions of concave symplectic fillings of all closed, oriented contact 3-manifolds. These constructions combine recent results of Giroux relating contact structures and open book decompositions of 3-manifolds, earlier results of the author on attaching 4-dimensiona…

Let $F_g$ denote a closed oriented surface of genus $g$. A set of simple closed curves is called a filling of $F_g$ if its complement is a disjoint union of discs. The mapping class group $\text{Mod}(F_g)$ of genus $g$ acts on the set of fillings of $F_g$. The union of the curves in a filling forms a graph on the surfa…

New length functions on mapping class groups linked to simplicial volumes of mapping tori.

We prove a general fusion theorem for complete orientable minimal surfaces in $\mathbb{R}^3$ with finite total curvature. As a consequence, complete orientable minimal surfaces of weak finite total curvature with exotic geometry are produced. More specifically, universal surfaces (i.e., surfaces from which all minimal …

The work of Jorgensen and Thurston shows that there is a finite number N(v) of orientable hyperbolic 3-manifolds with any given volume v. We show that there is an infinite sequence of closed orientable hyperbolic 3-manifolds, obtained by Dehn filling on the figure eight knot complement, that are uniquely determined by …

New groups formed by twists on surfaces are free.

A real 3- or 4-manifold has by definition an orientation preserving smooth involution acting on it. We consider Lefschetz fibrations of 4-dimensional manifolds-with-boundary and open book decompositions on their boundary in the existence of a real structure. We prove that there is a real open book which cannot be fille…

Study minima of geodesic lengths for specific curves on surfaces.