We use algebraic techniques to study homological filling functions of groups and their subgroups. If is a group admitting a finite --dimensional and is of type , then the --homological filling function of is bounded above by that of . This contrast with known examp…
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48 results for “homological filling function”
New filling functions for groups with coefficients show different asymptotic behavior.
problem Difficulty in filling loops with surfaces in Cayley graphs.
method Defining homological filling functions with coefficients and proving their differences.
result Filling functions for -cycles with coefficients in different groups have distinct asymptotic behavior.
The homological and homotopical Dehn functions are different ways of measuring the difficulty of filling a closed curve inside a group or a space. The homological Dehn function measures fillings of cycles by chains, while the homotopical Dehn function measures fillings of curves by disks. Since the two definitions invo…
The paper shows how coarse embeddings affect homological Dehn functions.
problem Characterizing groups with coarse embeddings into hyperbolic groups.
method Demonstrates a coarse embedding theorem for homological filling functions.
result Characterizes groups with coarse embeddings into hyperbolic groups of geometric dimension 2.
Research provides obstructions to Stein fillings of certain rational homology spheres.
problem Obstructing Stein fillings of specific rational homology spheres.
method Uses Pin(2)-monopole Floer homology.
result Provides obstructions to the intersection forms of Stein fillings.
The paper develops a method to construct left-orders on homology spheres from Dehn fillings.
problem Left-orderability of homology spheres obtained by Dehn filling.
method Holonomy extension loci of rational homology solid tori to study left-orderability.
result Intervals of Dehn fillings with left-orderable fundamental group.
Identifies Heegaard Floer homology solid tori via Dehn fillings.
problem Characterizing Heegaard Floer homology solid tori.
method Using Dehn fillings to identify solid tori.
result Characterized Seifert fibered Heegaard Floer solid tori.
In this article, using combinatorial techniques of mapping class groups, we show that a Stein fillable integral homology -sphere supported by an open book decomposition with page a -holed sphere admits a unique Stein filling up to diffeomorphism. Furthermore, according to a property of deforming symplectic fillin…
The paper bounds the smallest area of a minimal surface in 4D manifolds.
problem Finding the smallest area of minimal surfaces in 4D manifolds with specific curvature and volume constraints.
method The approach involves estimating the first homological filling function of the manifold.
result An upper bound for the area of a minimal surface is derived based on the manifold's properties.
Upper bound found for minimal area in Einstein 4-manifolds.
problem Finding the smallest area of a 2D varifold in closed Einstein 4-manifolds.
method Using homological filling functions and quantitative Sobolev and ε-regularity constants for Einstein metrics.
result An upper bound for the area of 2D varifolds in Einstein 4-manifolds.
Characterizes symplectic rational homology ball fillings of Seifert fibered spaces.
problem Understanding which Seifert fibered spaces can be boundaries of symplectic rational homology balls.
method Analyzes convex boundaries and Lagrangian disk fillings of Legendrian knots.
result Strong restrictions on which Seifert fibered spaces can bound symplectic rational homology balls.
The paper constructs homology spheres with large correction terms.
problem Finding homology spheres with large correction terms.
method Constructing families of homology spheres that bound 4-manifolds with intersection forms isomorphic to -E8.
result Homology spheres have arbitrarily large correction terms.
Study 2-complexes' homology properties and torsion growth.
problem Quantitative connections between 1-cycle filling inequalities and homology complexities.
method Geometric lower bounds on first homology of finite covers.
result Geometric lower bound on first homology size of finite covers.
We study the topology of exact and Stein fillings of the canonical contact structure on the unit cotangent bundle of a closed surface , where is at least 2. In particular, we prove a uniqueness theorem asserting that any Stein filling must be s-cobordant rel boundary to the disk cotangent bundle of . For …
We give an algorithm which produces infinitely many pairwise exotic Stein fillings of the same contact 3-manifolds, applying positive allowable Lefschetz fibrations over the disk. As a corollary, for a large class of Stein fillings, we realize the topological invariants (i.e. fundamental group, homology group, homology…
The paper explores conditions for homology spheres to bound acyclic smooth manifolds and symplectic fillings.
problem Conditions for integral homology 3-spheres to bound acyclic smooth 4-manifolds and their symplectic fillings.
method Structural results and analysis of smooth embeddings of lens spaces in .
result Smooth embeddings of connected sums of lens spaces in cannot be upgraded to Stein embeddings.
We apply representation theory to study the homology of equivariant Dehn-fillings of a given finite, regular cover of a compact 3-manifold with boundary a torus. This yields a polynomial which gives the rank of the part of the homology carried by the solid tori used for Dehn-filling. The polynomial is a symmetrized for…
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.
Torsion found in knot homology, challenging augmentation theories.
problem Torsion in linearized contact homology for Legendrian knots.
method Examples of Legendrian knots with non-trivial homology over Z.
result Augmentations not induced by exact fillings, even mod 2.
The study confirms the non-existence of rational homology ball symplectic fillings for certain Brieskorn spheres.
problem Non-existence of rational homology ball symplectic fillings for specific Brieskorn spheres.
method Analyzing contact structures and using obstruction techniques.
result Confirmation of non-existence for certain Brieskorn spheres.
Continuous sweepouts cover manifolds with bounded curve lengths.
problem Covering closed Riemannian manifolds with bounded curve lengths.
method Continuous family of 1-cycles parametrized by a sphere, with length bounds in terms of volume and dimension.
result Polyhedral 1-waist equals filling radius up to a constant factor.
Study shows exotic Dehn twists on certain 3-sphere fillings.
problem Extending group actions from boundaries to interiors of 4-manifolds.
method Analyzing Dehn twists on Seifert homology spheres and their fillings.
result Dehn twists on certain fillings are infinite order exotic.
Unique symplectic fillings for certain contact manifolds up to diffeomorphism.
problem Identifying unique symplectic fillings for contact manifolds.
method Analysis of a degree-theoretic evaluation map on a moduli space of holomorphic spheres.
result Simply connected contact manifolds with subcritical Stein fillings have a unique symplectically aspherical filling up to diffeomorphism.
New knots found without Lagrangian fillings.
problem Existence of Legendrian knots without Lagrangian fillings.
method Provided a family of Legendrian knots with augmentations not induced by any exact Lagrangian filling.
result Negative answer to the converse of the original statement.
New method yields sharp lower bounds for maps on tori and spheres.
problem Bounding homological size of maps on algebraic structures.
method Homological filling technique, applying isoperimetric inequalities.
result Sharp lower bounds for maps on tori and spheres.
The Euler class of taut foliations on Dehn fillings is studied, leading to new left-orderable slopes.
problem Analyzing the Euler class of taut foliations on Dehn fillings of a Q-homology solid torus.
method Developed a necessary and sufficient condition for the Euler class to vanish, applied to specific manifolds.
result Many new left-orderable Dehn filling slopes are obtained, including for pretzel knots.
Let M be a hyperbolic n-manifold whose cusps have torus cross-sections. In arXiv:0901.0056, the authors constructed a variety of nonpositively and negatively curved spaces as "2π-fillings" of M by replacing the cusps of M with compact "partial cones" of their boundaries. These 2π-fillings are closed pseudomanifolds, an…
We give a Khovanov homology proof that hyperbolic twist knots do not admit non-trivial Dehn surgeries with finite fundamental group.
Dehn filling rules Thurston norm for certain 3-manifolds.
problem Understanding Thurston norm behavior under Dehn filling.
method Analyzing slopes and Thurston norm for specific 3-manifolds.
result Thurston norm and winding norm relationship for Dehn filling.
The study shows knots from 3-braids cannot be concordant to a specific Legendrian unknot.
problem The concordance of knots from 3-braids to a specific Legendrian unknot.
method Using symplectic handlebody diagrams and Legendrian contact homology, the study derives a contradiction to show the non-concordance.
result The study proves that knots from 3-braids cannot be concordant to a specific Legendrian unknot.
The paper classifies symplectic fillings of lens spaces and constructs cobordisms.
problem Classifying symplectic fillings of lens spaces and constructing cobordisms.
method Analyzing tight and universally tight contact structures, using plumbing of disk bundles, and constructing cobordisms.
result Maximal second homology Stein fillings of lens spaces are given by specific plumbing.
New findings on Stein fillings and braids in 3D and 4D spaces.
problem Understanding Stein fillings and braids in contact 3-manifolds and 4-ball.
method Analyzing Stein fillings and Lefschetz fibrations, studying braids and their factorizations.
result Existence of infinitely many Stein fillings with distinct homology groups for certain contact 3-manifolds.
Paper stabilizes persistent homology rank functions for statistical inference.
problem Stability issues in persistent homology rank functions.
method Derive stability results for rank functions under FDA metrics.
result Rank functions stabilize, improving statistical inference.
New Stein fillings found for non-weighted homogeneous singularities.
problem Finding Stein fillings for certain non-weighted homogeneous singularities.
method Using spinal open books and nearly Lefschetz fibrations.
result Stein rational homology disk fillings for non-weighted homogeneous singularities.
New invariants show distinct contact structures have unique instanton homology.
problem Distinguishing contact structures on 3-manifolds using instanton Floer homology.
method Defined and used sutured instanton homology to prove contact invariants are linearly independent.
result Contact structures on 3-manifolds with distinct Chern classes have linearly independent contact invariants.
We construct a family of Stein fillable contact homology 3-spheres such that each contact structure of the family is supported by an open book with planar page, and a Stein filling of the contact manifold is of Mazur type.
We use contact handle decompositions and a stabilization process to compute the cylindrical contact homology of a subcritical Stein-fillable contact manifold with vanishing first Chern class, and show that it is completely determined by the homology of a subcritical Stein-filling of the contact manifold.
The paper classifies and studies symplectic and contact properties of circular spherical divisors.
problem Investigating symplectic and contact topology of circular spherical divisors.
method Classification and analysis of concave circular spherical divisors, including embedding, Stein fillability, and rational homology type determination.
result All concave circular spherical divisors up to toric equivalence are realized as symplectic log Calabi-Yau pairs with minimal complements.
The paper calculates critical points of systole function on Teichmüller space.
problem Critical points with pathological feature in surfaces of large genus.
method Integer linear programming with symmetry breaking technique.
result Found minimal filling sets of systoles in genus 5 with 8 geodesics.
New method shows some 3D shapes can't be filled in certain ways.
problem Obstructing Liouville and weak fillability of contact structures.
method Introducing a new method to obstruct fillability.
result Various rational homology 3-spheres admit strongly fillable contact structures without Liouville fillings.
For a 3-manifold with torus boundary admitting an appropriate involution, we show that Khovanov homology provides obstructions to certain exceptional Dehn fillings. For example, given a strongly invertible knot in S^3, we give obstructions to lens space surgeries, as well as obstructions to surgeries with finite fundam…
An L-space is a rational homology 3-sphere with minimal Heegaard Floer homology. We give the first examples of hyperbolic L-spaces with no symmetries. In particular, unlike all previously known L-spaces, these manifolds are not double branched covers of links in S^3. We prove the existence of infinitely many such examp…
The paper develops a method to create left-orders on fundamental groups of certain 3-manifolds.
problem Creating left-orders on fundamental groups of 3-manifolds.
method Using representations into and organizing them into a graph called the translation extension locus.
result Intervals of Dehn fillings of a compact 3-manifold with torus boundary have left-orderable fundamental groups.
We classify the resolution graphs of weighted homogeneous surface singularities which admit rational homology disk smoothings. The nonexistence of rational homology disk smoothings is shown by symplectic geometric methods, while the existence is verified via smoothings of negative weights. In particular, it is shown th…
The study explores Legendrian fillings and augmentations, providing methods to compute induced augmentations.
problem Understanding and computing Legendrian isotopy invariants through augmentations and fillings.
method Developed methods to compute induced augmentations based on Morse complex families and Legendrian cobordisms.
result Established methods to compute Legendrian isotopy invariants using augmentations and fillings.
Non-fibered L-space knotsmath.GT
We construct an infinite family of knots in rational homology spheres with irreducible, non-fibered complements, for which every non-longitudinal filling is an L-space.
Quantitative PL bordismmath.GT
Study PL bordism theories with quantitative bounds on filling simplices.
problem Understanding PL bordism theories with geometric constraints.
method Quantitative analysis of PL manifolds and exotic theories.
result Bounding the number of simplices in fillings of cycles.
On the involutive Heegaard Floer homology of negative semi-definite plumbed 3-manifolds with math.GT
The paper calculates involutive Heegaard Floer homology for specific 3-manifolds.
problem Calculating numerical invariants for specific 3-manifolds.
method Involutive Heegaard Floer homology techniques and spin filling constraints.
result Established new constraints and obstructions for 3-manifolds.