Knots in 4D manifolds are trivial based on Wedderburn's Theorem.
problem Understanding knots in 4-dimensional manifolds.
method Application of Wedderburn's Theorem.
result All knots and links in smooth 4D manifolds are trivial.
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48 results for “4D manifold”
We show that the smooth geometry of a hyperbolic 3-manifold emerges from a classical spin system defined on a 2d discrete lattice, and moreover show that the process of this "dimensional oxidation" is equivalent with the dimensional reduction of a supersymmetric gauge theory from 4d to 3d. More concretely, we propose a…
Study classifies special 4D shapes with certain curvature.
problem Classifying specific types of 4D shapes.
method Classifying compact almost-Kähler four manifolds with nonnegative biorthogonal curvature.
result Classified compact almost-Kähler four manifolds with nonnegative biorthogonal curvature.
The study calculates harmonic functions and 1-forms on specific 4D spaces.
problem Computing harmonic functions and 1-forms on ALE Ricci-flat 4-manifolds.
method Computed the expansion of harmonic functions and 1-forms.
result Computed the expansion of harmonic functions and 1-forms on ALE Ricci-flat 4-manifolds.
Study describes flat metric moduli spaces on 4D manifolds.
problem Understanding flat metrics on 4D closed manifolds.
method Algebraic and topological description of moduli spaces.
result Algebraic and topological description of moduli spaces of flat metrics.
Nearly Kaehler Reductionhep-th
We consider compactification of type IIA supergravity on nearly Kaehler manifolds. These represent a simple class of SU(3) structure manifolds which includes S^6 and CP^3. We exhibit for the first time an explicit reduction ansatz in this context, obtaining an N=2 gauged supergravity in 4d with a single vector and hype…
Geometric interpretation of 2d-4d wall-crossing formulas.
problem Understanding wall-crossing phenomena in coupled 2d-4d systems.
method Deformation theory of holomorphic pairs and relation to scattering diagrams.
result Geometric interpretation of wall-crossing formulas.
Study Higgs bundles for M-theory on G2-manifolds.
problem Understanding gauge theories coupled to gravity in M-theory compactifications.
method Derived BPS equations and massless spectrum using Morse and Morse-Bott theories.
result Determined Higgs bundle for TCS G2-manifolds and provided a prescription for chiral matter.
Researchers use manifold learning to analyze 4D-STEM data of graphene, revealing atomic structure details.
problem Challenges in processing and interpreting large 4D-STEM datasets, especially for light materials.
method Data-driven manifold learning approaches for visualization and exploration of 4D-STEM datasets.
result Extracted patterns relate to individual atom sites and sublattice structures, effectively discriminating single dopant anomalies.
Symmetrizes 4d and 3d BPS quivers for Argyres-Douglas theories.
problem Understanding the relationship between 4d and 3d BPS quivers.
method Analyzes geometric backgrounds and uses skein modules to derive quiver partition functions.
result Proves isomorphism between 4d wall-crossing and unlinking of symmetric quivers.
Study on flat metrics on 3D and 4D manifolds, focusing on topology and algebra.
problem Topology and algebraic structure of flat metrics on manifolds.
method Algebraic and topological descriptions of moduli spaces.
result Algebraic description and topology of moduli spaces for 4D manifolds with a single holonomy generator.
A class of 3d supersymmetric gauge theories are constructed and shown to encode the simplicial geometries in 4-dimensions. The gauge theories are defined by applying the Dimofte-Gaiotto-Gukov construction in 3d/3d correspondence to certain graph complement 3-manifolds. Given a gauge theory in this class…
Extends spectral Einstein functionals computation to 4D spin manifolds with boundary.
problem Computing spectral Einstein functionals for 4D spin manifolds with boundary.
method Generalizes Dabrowski's results to 4D spin manifolds with boundary using noncommutative residue.
result Generalized spectral Einstein functionals computation for 4D spin manifolds with boundary.
New curvature measures for 4D manifolds with corners defined and related to Gauss-Bonnet.
problem Defining curvature measures for 4D manifolds with corners.
method Defined two new extrinsic curvature quantities, one conformal invariant, and a new conformally invariant operator.
result Gauss-Bonnet theorem reformulated in terms of new curvature measures.
Study of essential conformal groups on Lorentzian manifolds, describing all 4D cases.
problem Understanding pseudo-Riemannian manifolds with transitive conformal groups.
method Spinor formalism and algebraic analysis.
result Construction and description of all 4D non conformally flat Lorentzian manifolds.
Study on 4D Lie groups and related almost hypercomplex manifolds.
problem Characterizing almost hypercomplex manifolds with specific metrics.
method Construction and classification of manifolds based on Lie algebras.
result Established a connection between Lie algebra classes and manifold classifications.
The paper studies 4D Ricci flow manifolds with curvature constraints.
problem Investigating 4D Ricci flow manifolds with specific curvature conditions.
method Analyzing 4D manifolds with curvature constraints via Ricci flow.
result Proves topological and geometric gap theorems for maximal volume growth.
New 4D examples show sphere equivalence doesn't imply isotopy.
problem Understanding when sphere equivalence implies topological isotopy in 4-manifolds.
method Constructing specific 4-manifolds with non-isotopic but equivalent 2-spheres.
result Gabai's 4D Lightbulb Theorem does not generalize to arbitrary 4-manifolds.
Study finds all 4D neutral manifolds.
problem Classifying neutral manifolds in four dimensions.
method Examined homogeneous semi-symmetric neutral manifolds.
result Identified all four-dimensional neutral manifolds.
The paper proves a spin manifold's 4D quasi-Einstein satisfies Hitchin-Thorpe inequality.
problem Proving a specific inequality for a class of 4D manifolds.
method Analyzing properties of gradient -quasi-Einstein manifolds, focusing on spin structures.
result Compact 4D spin gradient -quasi-Einstein manifolds satisfy the Hitchin-Thorpe Inequality when .
Perelman's proof confirmed, new method uses 4D topology.
problem Confirming the classical Poincaré conjecture.
method 4D topology, spun torus-knots, ribbonness, disk-chord system, Bing's result.
result Homotopy 3-sphere is diffeomorphic to the 3-sphere.
The study proves properties of 4D projective manifolds and builds non-hyperbolic examples.
problem Characterizing and understanding geometric properties of 4D projective manifolds.
method Analyzing geometric decompositions and using properties of locally symmetric spaces.
result Closed, indecomposable 4D projective manifolds are either real hyperbolic or have real hyperbolic pieces.
Classifies spin structures on 4D almost-flat manifolds.
problem Determining spin structures on almost-flat manifolds.
method Utilised the canonical orthogonal representation of fundamental groups.
result 15 out of 127 orientable families are non-spin.
Study on 4D manifolds with circulant structures and their products.
problem Characterizing 4D Riemannian manifolds with specific tensor structures.
method Investigation of Riemannian product manifolds with circulant structures and analysis of conditions for metric properties.
result Conditions for Riemannian product manifolds to belong to specific classes.
Proves biharmonic maps on 4D Einstein manifolds relate to Yamabe-type equations.
problem Constructing biharmonic conformal maps on 4D Einstein manifolds.
method Reduces biharmonic problem to Yamabe-type equations.
result Characterizes all solutions and constructs infinite family of examples.
The paper bounds the shortest closed geodesic length in 4D manifolds.
problem Finding the shortest closed geodesic in 4D manifolds with specific curvature and volume constraints.
method Utilizes recent theorems on diffeomorphism finiteness by J. Cheeger and A. Naber.
result The length of a shortest closed geodesic is bounded by a function that depends on volume and diameter .
Study uses superalgebra homology to classify 4D Engel-like Lie algebras.
problem Classifying 4-dimensional Engel-like Lie algebras.
method Applied homology groups of Lie superalgebras.
result Distinguished and classified 4D Engel-like Lie algebras.
This paper confirms volumes of geodesic balls can identify 4D space forms.
problem Determining if a 4D manifold is a space form using geodesic ball volumes.
method Tensor calculus and classical theorems, not topological characterizations.
result Similar results for 4D manifold space forms confirmed.
Explains how knots relate to 4D shapes.
problem Understanding 4D shapes through knot theory.
method Combines knot theory with 4D manifold topology.
result Connects 4D shapes to knot theory and other geometries.
David Gabai proves a 4D light bulb theorem using smooth techniques.
problem Constructive smooth 4-manifold theory advancements.
method Innovative use of classical moves in a smooth construction.
result First new hands-on advance in constructive smooth 4-manifold theory in a long time.
Researchers classify curvature homogeneous metrics on 4D manifolds.
problem Classifying curvature homogeneous metrics on 4D manifolds.
method Using equivariant diffeomorphisms and cohomogeneity one actions.
result Found that metrics are either symmetric or a specific example by Tsukada.
Research on the least complex surface in certain 4D shapes.
problem Finding the simplest surface in specific four-dimensional shapes.
method Analyzing smooth four-manifolds to determine minimal genus.
result Results on the minimal genus for studied four-manifolds.
For a fat sub-Riemannian structure, we introduce three canonical Ricci curvatures in the sense of Agrachev-Zelenko-Li. Under appropriate bounds we prove comparison theorems for conjugate lengths, Bonnet-Myers type results and Laplacian comparison theorems for the intrinsic sub-Laplacian. As an application, we consider …
Study second-Chern-Einstein metrics on 4D manifolds, finding Killing vector fields and examples.
problem Investigate second-Chern-Einstein metrics on 4D almost-Hermitian manifolds.
method Analyze compact and unimodular almost-abelian Lie algebras, use Killing vector fields and parallel non-zero Lee forms.
result Describe 4D compact second-Chern-Einstein locally conformally symplectic manifolds and classify unimodular almost-abelian Lie algebras with second-Chern-Einstein metrics.
Classifies special types of 4D spaces.
problem Classifying non-reductive 4D spaces.
method Classification based on conformal Einstein manifolds.
result Classification of non-reductive 4D homogeneous conformally Einstein manifolds.
Study of complex structures on product twistor spaces for 4D manifolds.
problem Understanding complex structures on product twistor spaces.
method Analyzing the product bundle of twistor spaces with Riemannian metrics and almost complex structures.
result Determined Gray-Hervella classes for 4D manifolds.
Study of black hole entropy from 4d theories on hyperbolic manifolds.
problem Determining the entropy of magnetically charged black holes in .
method Analytic torsions twisted by flat connections on hyperbolic 3-manifolds, perturbative expansion of index.
result The leading part of the index matches the Bekenstein-Hawking entropy of a magnetically charged black hole.
Quantum 4d Yang-Mills Theory and Time-Reversal Symmetric 5d Higher-Gauge Topological Field Theoryhep-th
New insights into 4d YM and 5d topological field theories with higher symmetries.
problem Exploring new topological field theories with higher symmetries.
method Dynamic gauging of 1-form symmetry, higher anomalies, and lattice simplicial complex regularizations.
result Discovery of new higher-form gauge fields and exotic anyonic statistics.
Study perturbs Dirac operator on 4D manifolds, proving Kastler-Kalau-Walze theorems.
problem Analyzing perturbations of Dirac operator on compact manifolds.
method Defining pseudo-differential perturbations and proving Kastler-Kalau-Walze theorems.
result Proved Kastler-Kalau-Walze theorems for 4D compact manifolds with boundary.
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.
The paper examines sequences of solutions to Seiberg-Witten systems in 4D manifolds.
problem Analyzing sequences of solutions to Seiberg-Witten systems in 4D manifolds.
method Investigates the behavior of sequences of solutions to Seiberg-Witten-like equations for Hermitian connections and spinor sections.
result Provides insights into the behavior of sequences of solutions to Seiberg-Witten systems in 4D manifolds.
Classifies flat compact Hermite-Lorentz 4D manifolds.
problem Classifying flat compact Hermite-Lorentz manifolds.
method Classification up to finite cover in complex dimension 4.
result Classification of flat compact Hermite-Lorentz 4D manifolds.
Study optimal transport in 4D sub-Riemannian spaces with many singular geodesics.
problem Existence and uniqueness of optimal transport maps in sub-Riemannian structures.
method Analysis of Monge optimal transport problem in sub-Riemannian manifolds.
result Extension of previous results to sub-Riemannian structures of rank two in 4D.
Paper studies critical points of curvature energies in 4D.
problem Critical points of conformally invariant extrinsic energies on 4-manifolds.
method Converted Euler-Lagrange equations to a system with favourable structures using invariances and Noether's theorem.
result Generalized Tristan Rivière's work on Willmore energy to 4D.
New -connection characterizes 4D spaces conformal to Einstein spaces.
problem Characterizing 4D spaces conformal to Einstein spaces.
method Introducing -connection, a Weyl connection that preserves conformal invariance.
result Characterizes non-degenerate spaces conformal to Einstein spaces.
No spin structures found in a hyperbolic 4D space.
problem Finding hyperbolic 4-manifolds without spin structures.
method Constructed a non-compact, orientable, hyperbolic 4-manifold.
result Demonstrated existence of a hyperbolic 4D space without spin structures.
We prove that a four-dimensional Lorentzian manifold that is curvature homogeneous of order 3, or $\CH_3$ for short, is necessarily locally homogeneous. We also exhibit and classify four-dimensional Lorentzian, $\CH_2$ manifolds that are not homogeneous.
New spines found in complex 4D shapes.
problem Finding spines in complex 4D shapes.
method Examined Levine and Lidman's constructions and found new spines.
result Infinitely many 4-manifolds have topological spines.