New proof shows rationality of scl for non-filling curves.
problem Understanding stable commutator length in non-filling curves.
method New proof using extremal surfaces for scl.
result Rationality of stable commutator length for non-filling curves.
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48 results for “filling surface”
Study fills a surface with odd, non-3 curves.
problem Determining filling pairs for surfaces with odd, non-3 punctures.
method Constructed minimally intersecting pairs of curves.
result Completed the classification of filling pairs for all surfaces.
Upper bounds on shortest filling geodesics on hyperbolic surfaces.
problem Finding the shortest geodesic that covers a surface.
method Quantitative density of closed geodesics on hyperbolic surfaces.
result Upper bounds on the length of the shortest closed geodesic.
This paper classifies and determines the length of the shortest filling pairs on a specific type of surface.
problem Classifying and determining the length of the shortest filling pairs on a specific type of surface.
method Classifying and determining the length of the shortest filling pairs on a specific type of surface.
result The paper classifies and determines the length of the shortest minimal filling pairs on a genus two surface.
The study creates Lefschetz fibrations for symplectic fillings of specific surface singularities.
problem Creating Lefschetz fibrations for symplectic fillings of quotient surface singularities.
method Constructing genus- or genus- positive allowable Lefschetz fibrations.
result Minimal symplectic fillings can be derived from rational blowdowns of their resolutions.
The paper constructs minimal coherent filling pairs on surfaces.
problem Finding minimal intersecting coherent filling pairs on surfaces.
method Geometric procedure starting from a torus filling pair.
result Construction of minimal intersecting coherent filling pairs on for .
Study Stein and Milnor fillings of links from surface singularities.
problem Comparing Stein and Milnor fillings of links from surface singularities.
method Analyzing the topology and obstructions of Stein fillings and Milnor fillings.
result Milnor fillings have bounded topology, while Stein fillings can be more varied.
Study on the minimum length of curves on once-punctured hyperbolic surfaces.
problem Finding the minimum length of filling pairs on once-punctured hyperbolic surfaces.
method Analyzing the topology and geometry of the surface to derive a lower bound for the length of filling pairs.
result A lower bound for the length of filling pairs on once-punctured hyperbolic surfaces is derived, depending only on the surface's topology.
We show that after generic filling along a torus boundary component of a 3-manifold, no two closed, 2-sided, essential surfaces become isotopic, and no closed, 2-sided, essential surface becomes inessential. That is, the set of essential surfaces (considered up to isotopy) survives unchanged in all suitably generic Deh…
The study proves nearly geodesic surfaces are filling in hyperbolic 3-manifolds.
problem Proving nearly geodesic surfaces are filling in hyperbolic 3-manifolds.
method Using quasi-Fuchsian surfaces and totally geodesic surfaces, the study proves filling properties with rigorous mathematical proofs.
result Proves nearly geodesic surfaces are filling in hyperbolic 3-manifolds.
Let be a closed surface of genus and let be a filling pair on ; then , where is the (geometric) intersection number. Aougab and Huang demonstrated that (exponentially many) minimally-intersecting filling pairs exist on when by a construction w…
New surfaces with few filling systoles found.
problem Finding surfaces with a small number of systoles that still fill.
method Constructing a hyperbolic surface with a specified number of systoles that fill.
result Disproved the lower bound on systole count for filling surfaces.
New method for calculating loop operations on surfaces.
problem Computing algebraic operations on loops in surfaces.
method Using fillings of surfaces by graphs to compute homological intersection number, Lie bracket, and Lie cobracket.
result Effective new approach to standard algebraic operations on loops.
Symplectic fillings of surface singularities linked to minimal model program.
problem Symplectic fillings of quotient surface singularities.
method Sequence of rational blow-downs and symplectic antiflips.
result Every minimal symplectic filling can be obtained from minimal resolution via rational blow-downs and antiflips.
Paper finds minimal number of curves in surface systems.
problem Determining minimal number of curves in surface systems.
method Analyzes oriented surfaces of genus g for positive integers k and g.
result Exact minimal number of curves in filling k-systems.
This paper tackles Gromov's filling area conjecture using discrete graph theory.
problem Finding the smallest surface area for isometrically filling a circle.
method Using graph-theoretic tools like Menger's theorem to derive bounds.
result Discrete bounds translate to a lower bound of 1.36π for the hemisphere's surface area.
This paper is about the geometry of flip-graphs associated to triangulations of surfaces. More precisely, we consider a topological surface with a privileged boundary curve and study the spaces of its triangulations with n vertices on the boundary curve. The surfaces we consider topologically fill this boundary curve s…
In this paper, we use normal surface theory to study Dehn filling on a knot-manifold. First, it is shown that there is a finite computable set of slopes on the boundary of a knot-manifold that bound normal and almost normal surfaces in a one-vertex triangulation of that knot-manifold. This is combined with existence th…
New approach finds minima of geodesic lengths for non-uniform fillings.
problem Finding minima of geodesic length functions for non-uniform fillings.
method Elementary optimization for 4-regular topological fillings, analysis of fat graphs and optimization techniques.
result Minima of geodesic length functions are found to be at triangle surfaces in both analyzed classes of non-uniform fillings.
The article finds conditions for separating filling pairs on surfaces and constructs a Morse function.
problem Conditions for separating filling pairs on surfaces.
method Combinatorial study of mapping class group action and construction of a Morse function.
result Cardinality of global minima of the Morse function equals the number of orbits of filling pairs.
We prove that any minimal weak symplectic filling of the canonical contact structure on the unit cotangent bundle of a nonorientable closed surface other than the real projective plane is s-cobordant rel boundary to the disk cotangent bundle of the surface. If the nonorientable surface is the Klein bottle, then we show…
When a Dehn filled link manifold contains a geometrically incompressible one-sided surface, it is shown there is a unique boundary incompressible position that the surface can take in the link space. The proof uses a version of the sweep-out technique from two-sided Heegaard splitting theory. When applied to one-sided …
Algorithm decides if geodesic curves are filling on surfaces.
problem Determining if geodesic curves are filling on surfaces.
method Efficient algorithm using Dehn-Thurston coordinates and combinatorial length bounds.
result Explicit bound for combinatorial length in terms of hyperbolic length.
The paper classifies minimal symplectic fillings of small Seifert 3-manifolds.
problem Classifying minimal symplectic fillings of small Seifert 3-manifolds.
method Using rational blowdowns and weighted homogeneous complex surface singularities.
result Every minimal symplectic filling of small Seifert 3-manifolds is obtained by a sequence of rational blowdowns.
New Stein fillings found for rational surface singularities.
problem Exploring Stein fillings of rational surface singularities.
method Using planar open books and Lefschetz fibrations, describe Stein fillings via symplectic disk arrangements.
result Many rational singularities admit Stein fillings not diffeomorphic to Milnor fibers.
We study symplectic deformation types of minimal symplectic fillings of links of quotient surface singularities. In particular, there are only finitely many symplectic deformation types for each quotient surface singularity.
The paper fills hyperbolic surfaces with a minimal number of systoles.
problem Finding the minimum number of systoles to fill a hyperbolic surface.
method The approach is simpler than previous methods, using systoles.
result The number of systoles needed is .
Maximizes filling systems on surfaces with given boundary components.
problem Finding the maximum size of filling systems on surfaces with specific boundary conditions.
method Analyzing the structure of filling systems and their complements.
result The maximum size of a filling system on a surface of genus g with 1 ≤ b ≤ 2g-2 boundary components is 2g + b - 1.
New rays on infinite type surfaces help understand their boundaries.
problem Describe the boundary of the loop graph of infinite type surfaces.
method Combining combinatorial and geometric approaches, constructing 2-filling rays.
result Constructed the first examples of 2-filling rays on infinite type surfaces.
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…
We prove results showing that the existence of essential maps of surfaces in a manifold M' obtained from a 3-manifold M by Dehn filling implies the existence of essential maps of surfaces in M.
Filling systems on surfacesmath.GT
Maximizes the number of curves needed to cover a surface without overlapping.
problem Finding the maximum number of curves needed to cover a surface without overlapping.
method Analyzing the geometric intersection numbers of curves in minimal fillings.
result Maximum size of a filling of a surface is 2g + b - 1.
Paper proves a conjecture about the minimum length of filling pairs on hyperbolic surfaces.
problem Finding the minimum length of filling pairs on hyperbolic surfaces.
method Proves a generalized isoperimetric inequality for disconnected regions.
result Proves the Aougab-Huang conjecture about the minimum length of filling pairs.
Banchoff's sphere splits trefoil knots in 3-manifolds.
problem Understanding how Dehn spheres split trefoil knots in 3-manifolds.
method Constructing and analyzing filling Dehn spheres and their diagrams.
result Banchoff's sphere splits the trefoil knot in .
The study of symplectic fillings for rational cuspidal curves.
problem Understanding symplectic fillings of contact manifolds associated with rational cuspidal curves.
method Exploration through Stein handlebodies and rational blow-downs.
result Examples of contact manifolds that are links of normal surface singularities, and those that do not admit symplectic fillings.
Study minima of geodesic lengths for specific curves on surfaces.
problem Finding the shortest geodesic paths on surfaces.
method Using curves related to dessins d'enfants and Grothendieck-Belyi surfaces.
result Minima of geodesic lengths are achieved on Riemann surfaces defined over number fields.
Filling of closed Surfacesmath.GT
Let denote a closed oriented surface of genus . A set of simple closed curves is called a filling of if its complement is a disjoint union of discs. The mapping class group of genus acts on the set of fillings of . The union of the curves in a filling forms a graph on the surfa…
New metric on geodesic currents connects different surface genera.
problem Understanding geodesic currents on surfaces of varying genera.
method Introducing a new asymmetric metric on the space of projective filling geodesic currents.
result Metric spaces of projective filling geodesic currents for surfaces of different genera are not isometric.
New groups formed by twists on surfaces are free.
problem Understanding groups formed by Dehn twists on surfaces.
method Finding specific fillings that generate free groups.
result Groups generated by twists are free for certain configurations.
We study filling sets of simple closed curves on punctured surfaces. In particular we study lower bounds on the cardinality of sets of curves that fill and that pairwise intersect at most k times on surfaces with given genus and number of punctures. We are able to establish orders of growth for even k and show that for…
If a hyperbolic 3-manifold admits an exceptional Dehn filling, then the length of the slope of that Dehn filling is known to be at most six. However, the bound of six appears to be sharp only in the toroidal case. In this paper, we investigate slope lengths of other exceptional fillings. We construct hyperbolic 3-manif…
The study examines dynamics on SU(2)-representation varieties for surfaces and non-orientable surfaces.
problem Dynamics of group actions on SU(2)-representation varieties of surfaces and non-orientable surfaces.
method Description and analysis of group actions generated by Dehn twists on SU(2)-representation varieties.
result Explicit invariant rational functions on SU(2)-representation varieties for specific cases of surfaces and non-orientable surfaces.
The study finds infinitely many Lagrangian fillings for most Legendrian torus links.
problem Infinitely many Lagrangian fillings for Legendrian torus links except for a few.
method Constructing infinite order Lagrangian concordances and using actions of modular and mapping class groups.
result There exist infinitely many Lagrangian fillings for most Legendrian torus links.
New proof shows unique symplectic fillings for certain surface singularity links.
problem Uniqueness of symplectic fillings for specific rational surface singularity links.
method Analysis of positive monodromy factorizations for planar open books.
result Unique symplectic fillings proven for specified contact structures.
Study irrational rotations and construct 2-filling rays on infinite type surfaces.
problem Understanding dense orbits in skew product transformations.
method Skew product transformation with continued fraction analysis.
result Existence of infinite cliques of 2-filling rays on infinite type surfaces.
Small sets of systoles fill hyperbolic surfaces of large genus.
problem Constructing hyperbolic surfaces with minimal systole sets.
method Theory of Coxeter groups combined with number theory.
result Cardinality of systole sets is in o(g/ ln g) for large genus.
We give a summary of known results on the maximal distances between Dehn fillings on a hyperbolic 3-manifold that yield 3-manifolds containing a surface of non-negative Euler characteristic that is either essential or Heegaard.
Proves left-orderability of certain Dehn fillings on 3-manifolds.
problem Left-orderability of Dehn fillings on 3-manifolds.
method Constructing arcs of representations and using holonomy extension techniques.
result Establishes intervals of orderable Dehn fillings for odd pretzel knots.