Paper compares and intersects classes in Johnson cokernels of surface mapping groups.
problem Comparing and intersecting classes in Johnson cokernels of mapping class groups of surfaces.
method Representation theoretic and topological approaches.
result Anti-Morita obstructions and hook-type components appear in the Johnson cokernels.
This paper studies torsion obstructions to complex sections on manifolds.
problem Torsion obstructions to finding complex sections on almost complex manifolds.
method Calculations using the Adams-Novikov spectral sequence for Thom spectra.
result Torsion obstructions for finding r complex sections of order p vanish for r<p2−p. Describes Wall's finiteness obstruction.
problem Finiteness obstruction in algebraic topology.
method Self-contained description of Wall's finiteness obstruction.
result Comprehensive explanation of Wall's finiteness obstruction.
New obstructions for knots in high dimensions prevent double sliceness.
problem Preventing double sliceness of knots in high dimensions.
method Developed L(2)-signature obstructions for metabelian knot groups. result Found infinite families of knots not obstructed by previous invariants.
Fewer obstructions for small graphs in knotless embedding.
problem Finite obstructions for knotless embedding of small graphs.
method Analysis of graph minor obstructions and knotless embedding.
result There are only three obstructions for size 23 graphs, significantly fewer than previously known.
3028 obstructions found for embedding without knots.
problem Finding obstructions for knotless embedding.
method Surveying recent work, updating obstructions, and proposing new questions.
result New obstructions with μ=6 and insights into connectivity.
Obstructing deformations of vector forms on Kähler manifolds.
problem Deformations of vector forms on compact Kähler manifolds.
method Annihilating obstruction classes by cohomology classes.
result Obstruction classes are annihilated by cohomology classes.
Study calculates Euler obstruction for determinantal varieties with ICIS singular set.
problem Calculating Euler obstruction for determinantal varieties with ICIS singular set.
method Obtained formulas to calculate Euler obstruction for determinantal varieties with ICIS singular set.
result Formulas to calculate the Euler obstruction for determinantal varieties with ICIS singular set.
The paper develops obstructions for embedding 2D complexes into 4D space.
problem Embedding 2D complexes into 4D space and understanding obstructions.
method Uses Goodwillie-Weiss calculus and intersections of Whitney disks.
result Two approaches to obstructions lead to the same result.
Global obstructions found for conformally Einstein metrics in 6D.
problem Obstructing the existence of conformally Einstein metrics in six dimensions.
method Presentation of global conformal invariants.
result Nontrivial global conformal invariant obstructing conformally Einstein metrics.
Complete surgery obstructions for manifolds with finite fundamental group, disproving a conjecture.
problem Disproving the Oozing Conjecture for manifolds with finite fundamental group.
method Description and calculation of surgery obstructions up to homotopy equivalence.
result New obstructions found for Arf invariant product formulas in codimensions ≥ 4, disproving the Oozing Conjecture.
Given a polarized manifold there are obstructions for asymptotic Chow semistability described as integral invariants. One of them is an obstruction to the existence for the first Chern class of the polarization to admit a constant scalar curvature Kähler (cscK) metric. A natural question is whether or not the other obs…
The article classifies cubiquitous sublattices and applies them to branched covers.
problem Understanding cubiquitous sublattices as obstructions to rational homology 4-balls.
method Developed a geometric Wu obstruction to classify cubiquitous sublattices and applied it to branched covers.
result Completely classified which sublattices with orthogonal bases are cubiquitous.
New obstructions found for smooth desingularization of compact Einstein orbifolds.
problem Finding obstructions to desingularizing compact Einstein orbifolds.
method Identifying new obstructions specific to compact Einstein 4-orbifolds. result Almost all flat orbifold metrics on T4/Z2 are not limits of Ricci-flat metrics. Study uses braid conjugacy class invariants to find ribbon obstructions for knots.
problem Finding effective obstructions for slice knots to be ribbon.
method Apply Rudolph's work and Khovanov-Lee theory to braid conjugacy class invariants.
result Cannot obtain effective ribbon obstructions using Khovanov-Lee theory.
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…
Study surgery obstructions for Seifert fibered homology spheres using knot and Heegaard Floer homology.
problem Determining which knots can yield Seifert fibered homology spheres.
method Utilized Heegaard Floer and Knot Floer homology, along with the mapping cone formula, to find obstructions.
result Showed that genus one knots cannot yield Seifert fibered homology spheres with six or more singular fibers.
Study identifies obstructions for solving a 4th-order boundary problem.
problem Solving a 4th-order boundary problem with specific curvature conditions.
method Derived Kazdan-Warner type identities using variational formulation and conformal variations.
result Obtained nontrivial integral obstructions to solvability.
Developing a singular dimension descent method for positive scalar curvature obstructions
problem Positive scalar curvature obstructions in arbitrary dimensions
method Schoen--Yau type singular dimension descent method
result Proving obstructions to positive scalar curvature on enlargeable manifolds
Study Euler obstruction of 1-forms on determinantal singularities.
problem Understanding the Euler obstruction of 1-forms on determinantal singularities.
method Investigation of connections between local Euler obstruction and PHN index.
result Explicit computations of Euler obstruction for specific singularities.
The paper explores properties of CR hypersurfaces and their flatness.
problem Analyzing the flatness properties of CR hypersurfaces.
method Investigation of local and global properties of strongly pseudoconvex CR hypersurfaces.
result Existence of obstruction flat points on compact CR hypersurfaces.
Proves Massey's theorems on complex structure obstructions.
problem Finding complex structures on real vector bundles.
method Fractional Stiefel-Whitney classes and combinations of Pontryagin, Chern, and Euler classes.
result Determines the second obstruction for rank six bundles.
Study on a specific obstruction in four-dimensional geometry.
problem Singular Yamabe obstruction of a hypersurface.
method Derived various explicit formulas from the original definition.
result Relate formulas to literature and prove elementary.
The paper explores obstructions for symplectic Lie algebroids on surfaces.
problem Obstacles to the existence of symplectic Lie algebroids.
method Analysis through characteristic classes of symplectic Lie algebroids.
result Full obstructions for surfaces to carry symplectic Lie algebroids.
Introduce generalized Ueda obstruction classes for line bundles and apply them to non-semi-positivity.
problem Non-semi-positivity of line bundles
method Introduce generalized Ueda obstruction classes and use Dolbeault resolution
result Recover classical examples and provide new examples of nef but not semi-positive line bundles
Surgery obstructions extended to integer homology spheres using Heegaard Floer homology.
problem Obstructing knots in integer homology spheres using surgery.
method Extending Heegaard Floer homology obstructions to all integer homology spheres for both positive and negative surgeries.
result Deduced a lower bound on b2(W) for smooth cobordism between integer homology spheres. Extended solitons show constant curvature on compact manifolds.
problem Understanding self-similar solutions to geometric flows.
method Analyzing extended solitons and applying integral inequalities.
result Closed ambient obstruction solitons are ambient obstruction flat and have constant scalar curvature.
Study the topological information of map germs using Euler obstruction.
problem Capturing topological information from map germs with complex singular spaces.
method Investigates the Euler obstruction and its relation to local Euler obstruction and Brasselet number.
result Relates Chern number to the number of cusps in a perturbed map-germ.
Paper proves how 3D shapes can be embedded without obstructions.
problem Embedding 2D shapes in 3D space without crossing.
method Analogue of Kuratowski's graph planarity theorem for 3D.
result Finite list of obstructions except one infinite family.
New obstructions show some 4-manifold homeomorphisms are pseudo-isotopic but not isotopic.
problem Tackling the difference between pseudo-isotopy and isotopy for 4-manifolds.
method Defining and showing realizable obstructions in Whitehead groups.
result Found homeomorphisms that are pseudo-isotopic but not isotopic.
Geometrically, a new obstruction is found for 4-manifold realizations.
problem Realizing normal 1-types of 4-manifolds with a given boundary.
method Three-stage obstruction theory, with a geometric tertiary obstruction.
result A new geometric tertiary obstruction for 4-manifold realizations.
New curvature obstruction for Killing vector fields on Lorentzian manifolds.
problem Existence of timelike or causal Killing vector fields on Lorentzian manifolds.
method New curvature obstruction in terms of timelike or null sectional curvature.
result Extension of Gauss-Bonnet-Chern obstruction to non-zero timelike sectional curvature.
Study torsion obstructions to positive scalar curvature on manifolds.
problem Obstructions to positive scalar curvature metrics on manifolds.
method Analysis of torsion classes in integral homology.
result Construction of manifolds without positive scalar curvature metrics but whose Cartesian products do.
Survey paper examines obstructions to solving Kähler geometry problems.
problem Existence of Kähler-Ricci solitons, Sasaki-Einstein metrics, and conformally Einstein-Maxwell Kähler metrics.
method Obstructions are derived as derivatives of volume functionals for vector fields.
result Identifies vector fields for which existence problems should be attempted.
Study integral bounds for submanifolds in low codimension with topological implications.
problem Integral curvature bounds and topological obstructions for submanifolds.
method Integral curvature bounds in terms of Betti numbers, δ-pinched immersions, and pinched second fundamental form. result Obtained topological obstructions for δ-pinched immersions and intrinsic obstructions for minimal submanifolds in spheres. Develops formal moduli theory for splitting complex supermanifolds.
problem Tackles the splitting problem of complex supermanifolds.
method Constructs a filtered dg Lie algebra to control splittings and transfers the theory to a minimal filtered L∞-model. result Recover classical obstruction classes as leading terms of Maurer-Cartan representatives and proves the existence of higher obstructions.
The paper shows examples of 2-complexes that can't be embedded in R^4, hiding obstructions in higher Milnor invariants.
problem Embedding 2-complexes in R^4 with hidden obstructions.
method Provides examples of 2-complexes and families of PL immersions that hide embedding obstructions.
result Embedding obstructions vanish for the given examples, answering a question in Avramidi-Okun-Schreve's paper.
We describe two simple obstructions to the existence of Ricci-flat Kahler cone metrics on isolated Gorenstein singularities or, equivalently, to the existence of Sasaki-Einstein metrics on the links of these singularities. In particular, this also leads to new obstructions for Kahler-Einstein metrics on Fano orbifolds.…
Study pseudoisotopies in 4-manifolds, finding specific elements of obstruction.
problem Understanding pseudoisotopies in 4-manifolds.
method Explicit construction of pseudoisotopies for certain elements of the second obstruction.
result Explicit construction of pseudoisotopies for specific elements of the second obstruction.
Obstructs Legendrian knots from being slices of concordances using doubly slice genus.
problem Obstructing Legendrian knots from being slices of concordances.
method Uses Eliashberg and Polterovitch's result on doubly slice genus as an obstruction.
result Obstructs Legendrian knots from being slices of concordances, including examples of Pretzel knots.
Applying a local Gauss-Bonnet formula for closed subanalytic sets to the complex analytic case, we obtain characterizations of the Euler obstruction of a complex analytic germ in terms of the Lipschitz-Killing curvatures and the Chern forms of its regular part. We also prove analogous results for the global Euler obstr…
Obstructions found for closed Fedosov star products on symplectic and Kähler manifolds.
problem Existence of closed Fedosov star products on symplectic and Kähler manifolds.
method Normalized trace of Fedosov star product, cohomology classes, and formal 2-forms.
result Integral invariants attached to symplectic and Kähler manifolds as obstructions to closed Fedosov star products.
Computes homology of an obstruction chain complex in grid homology.
problem Computing the homology of an obstruction chain complex in grid homology.
method Defined and computed the homology of the obstruction chain complex of the full grid.
result Results about the existence of sign assignments in grid homology.
Formula found for Kähler-Einstein metric existence obstruction.
problem Obtaining Kähler-Einstein metrics on manifolds.
method Residue formula for Futaki-Zhang obstruction.
result Found coupled Kähler-Einstein metrics on a specific toric Fano manifold.
The (Fefferman-Graham) ambient obstruction tensor is a conformally invariant symmetric trace-free 2-tensor on even-dimensional Riemannian and pseudo-Riemannian manifolds. The conformal deformation complex is a differential complex related to infinitesimal deformations of conformal structure. We construct a conformally …
We show that any asymptotically locally Euclidean (ALE) metric which is obstruction-flat or extended obstruction-flat must be ALE of a certain optimal order. Moreover, our proof applies to very general elliptic systems and in any dimension n≥3. The proof is based on the technique of Cheeger-Tian for Ricci-flat m…
Integrates transitive Lie algebroids to Lie groupoids, explaining obstructions.
problem Integrating transitive Lie algebroids to Lie groupoids.
method Geometric explanation and explicit construction of integration, with obstructions considered.
result Obstructions explained and integration constructed when they vanish.
Paper detects duality obstruction in smooth calibrations.
problem Detecting duality obstruction in smooth calibrations.
method Examine Lawlor cones and calibrations, use gluing results.
result Existence of Lawlor cones without smooth calibrations.