Embeds 3-manifolds in symplectic 4-manifolds with constraints.
problem Embedding 3-manifolds in symplectic 4-manifolds with topological and smooth properties.
method Topological and smooth embeddings, using homology cobordism and obstructions.
result 3-manifolds can be embedded in symplectic 4-manifolds with specific conditions.
Survey on embedding 3-manifolds in definite 4-manifolds, focusing on Donaldson's theorem.
problem Understanding embeddings of 3-manifolds in definite 4-manifolds.
method Utilizes Donaldson's diagonalization theorem and combinatorics of integral lattices.
result New result on embedding amphichiral lens spaces in negative-definite manifolds.
Minimal dimensions found for flag manifolds embeddings.
problem Finding the smallest dimensions for flag manifolds embeddings.
method Equivariant embeddings of orthogonal and unitary groups acting on real and complex flag manifolds.
result Minimal dimensions achieved at isospectral models.
The study finds minimal volume hyperbolic 4-manifolds with embedded 3-manifolds.
problem Existence of small volume hyperbolic 4-manifolds with embedded 3-manifolds.
method Analysis of hyperbolic manifolds and their submanifolds.
result Minimal volume hyperbolic 4-manifolds with embedded 3-manifolds exist.
Long spacelike embeddings can be approximated by isometric ones.
problem Approximating long embeddings to isometric embeddings in Lorentzian spaces.
method Proving approximation by constructing C 1 C^1 C 1 isometric embeddings. result Long spacelike embeddings can be C 0 C^0 C 0 -approximated by C 1 C^1 C 1 isometric embeddings. Study on fundamental groups of framed circle embeddings in 4-manifolds.
problem Understanding the fundamental groups of spaces of framed embeddings of a circle in 4-manifolds.
method Investigates the fundamental groups of spaces of embeddings of S 1 i m e s D 3 S^1 imes D^3 S 1 im es D 3 in 4-manifolds, focusing on framed immersed circles. result Investigates the fundamental groups of spaces of framed embeddings of a circle in 4-manifolds, providing insights into the structure of these groups.
Study symplectic embeddings of 4-manifolds using Lefschetz fibrations.
problem Proper symplectic and iso-symplectic embeddings of 4-manifolds in 6-manifolds.
method Use Lefschetz fibrations to study symplectic embeddings.
result Closed orientable smooth 4-manifolds admitting Lefschetz fibrations over CP^1 can be embedded symplectically in (CP^1 × CP^1 × CP^1, ω_pr).
New families of embeddings in 4-manifolds, topologically trivial but smoothly non-trivial.
problem Constructing non-trivial smooth embeddings of 3-manifolds in 4-manifolds.
method Parameterized families of embeddings, using high-dimensional spheres.
result Embeddings of homology spheres and any 3-manifold in blown-up K3 surfaces.
Curvature regularization prevents distortion in graph embeddings.
problem Graph topology patterns distort in Euclidean space, making detection difficult.
method Proposes curvature regularization to enforce flatness in embedding manifolds.
result Significant improvements in five embedding methods on open graph datasets.
Embeds pre-multisymplectic manifolds into coisotropic ones.
problem Embedding pre-multisymplectic manifolds.
method Proves a coisotropic embedding theorem.
result Validates embedding of pre-multisymplectic manifolds.
The abstract discusses embedding manifolds in open books and contact structures.
problem Embedding manifolds in open books and contact structures.
method Using open book embeddings and contact structures, the abstract proves embedding theorems for various manifolds.
result Closed manifolds can be embedded in open books and contact structures.
Proves uniqueness of embedding complex manifold into infinite-dimensional space.
problem Balanced embedding of non-compact complex manifold into infinite-dimensional projective space.
method Fine estimates of asymptotics of a balanced embedding.
result Uniqueness of embedding proven.
Study on embedding surfaces into 3-manifolds, focusing on equivariant cases.
problem Embedding hyperbolic surfaces into hyperbolic 3-manifolds with specific symmetries.
method Examined orientation-preserving and orientation-reversing actions on surfaces, including nonorientable ones.
result Found conditions for equivariant embeddings of hyperbolic surfaces into hyperbolic 3-manifolds.
Tubes in manifolds require wide spaces.
problem Embedding constraints in Riemannian manifolds.
method Analyzing uniformly thick tubular neighborhoods.
result Conditions for manifold embeddings with wide tubes.
Notes on embedding criteria for smooth manifolds.
problem Conditions for embedding smooth manifolds into Euclidean space.
method Linking recent results to classical criteria and K-theory.
result Recent results connect to classical embedding criteria.
3-manifolds with two abelian-filled spaces.
problem Finding 3-manifolds with multiple abelian-filled spaces.
method Constructing 3-manifolds with specific embedding properties.
result 3-manifolds with at least two abelian-filled spaces.
The Bonnet theorem is proven for statistical manifolds.
problem Locally embeddable statistical manifolds in flat spaces.
method Using statistical embedding and the Gauss--Codazzi--Ricci equations.
result Statistical manifolds with specific tensor properties are locally embeddable to flat statistical manifolds.
New embeddings for manifolds using heat kernels.
problem Constructing canonical conformal embeddings for manifolds.
method Employing heat kernel embedding from Bérard-Besson-Gallot'94 to find canonical conformal embeddings.
result Intrinsic construction of canonical conformal embeddings with dimensions growing exponentially with t t t . The study characterizes and verifies equivariant embeddings of symmetric Kählerian manifolds.
problem Characterizing and verifying equivariant embeddings of symmetric Kählerian manifolds.
method Investigation motivated by Cartan and Wallach's theorem on symmetric spaces, focusing on C P n \mathbb{CP}^n CP n and parallel plurimean curvature. result If an equivariant embedding has parallel plurimean curvature, it is the extrinsically symmetric one.
We consider a compact connected CR manifold with a transversal CR locally free R \mathbb R R -action endowed with a rigid positive CR line bundle. We prove that a certain weighted Fourier-Szegő kernel of the CR sections in the high tensor powers admits a full asymptotic expansion and we establish R \mathbb R R -equivariant K…
Proposes QQE for transforming and embedding data distributions.
problem Transforming and embedding data distributions for better representation or visualization.
method Quantile-Quantile Embedding (QQE) using quantile-quantile plot concept.
result QQE allows for better discrimination of classes in some cases.
Smoothly embed 3-manifolds in 5-manifolds, simplifying topological to smooth.
problem Embedding 3-manifolds smoothly in 5-manifolds.
method Homotopy and small homotopy to achieve smooth embeddings.
result Locally flat embeddings are homotopic to smooth ones.
Smoothly approximates embeddings in Lorentzian manifolds.
problem Approximating embeddings in Lorentzian manifolds.
method C^0 approximation of embeddings.
result Approximated embeddings can be made smooth.
Paper proves embedding theorem for conformally compact manifolds.
problem Embedding conformally compact manifolds into hyperbolic spaces.
method Proves analogous Nash Embedding Theorem for conformally compact manifolds.
result Conformally compact manifolds can be isometrically embedded into hyperbolic spaces.
Study rational homotopy types of embedding spaces of manifolds.
problem Understanding the rational homotopy types of embedding spaces of manifolds.
method Express rational homotopy types through combinatorially defined L-infinity algebras of diagrams.
result Expressed the rational homotopy type of connected components of embedding spaces.
Condition for embedding metric spaces into curved manifolds.
problem Embedding conditions for metric spaces in curved manifolds.
method If-and-only-if condition on five-point metric spaces.
result Five-point metric spaces admit embeddings into nonnegatively curved Riemannian manifolds.
MEDAL converts manifold embeddings into models for rigorous validation.
problem Challenges in validating manifold embeddings without held-out validation.
method Develops MEDAL framework that distills embeddings into autoencoder models.
result Enables rigorous validation of manifold embeddings and hyperparameters.
Solves embedding problem for 5D manifolds into Calabi-Yau 3-folds.
problem Embedding a 5D manifold into a Calabi-Yau 3-fold with a specific 3-form.
method Defines 'strongly pseudoconvex' 3-forms and shows solvability of embedding problem for these forms under certain conditions.
result Perturbative embedding problem can be solved for closed strongly pseudoconvex 3-forms if a vector space of obstructions vanishes.
Study of codimension-1 embeddings in 3-manifolds using twist maps and push maps.
problem Embedding 3-manifolds in specific topological spaces.
method Sphere twist maps and push maps to construct codimension-1 spun embeddings.
result Every closed orientable 3-manifold admits a codimension-1 spun embedding in specific spaces.
Study explores embedding signature-changing manifolds into higher-dimensional spaces.
problem Smooth metric signature changes in spacetimes.
method Global isometric embeddings into higher-dimensional pseudo-Euclidean spaces.
result Explicit constructions of global embeddings into Minkowski and Misner spaces.
New framework for manifold convolutions using toric embeddings.
problem Computational intractability of manifold convolutions.
method Isometric embeddings into tori for global manifold convolutions.
result Global definition of manifold convolutions on finite approximations.
This paper proves the existence of a smooth embedding for symmetrical manifolds.
problem Embedding symmetrical Riemannian manifolds isometrically in Euclidean spaces.
method Proves the existence of a C ∞ C^\infty C ∞ equivariant isometric embedding. result Existence of a C ∞ C^\infty C ∞ equivariant isometric embedding of M M M in $\RR^q$ . We obtain estimations for isotopy classes of embeddings of closed k-connected n-manifolds into R^{2n-k-1} for n>2k+5 and k\ge0. This is done in terms of an exact sequence involving the Whitney invariants and an explicitly constructed action of H_{k+1}(N;Z_2) on the set of embeddings. (For k\ne1 classification results w…
This paper proves the manifold hypothesis for lower embedding dimensions using osculating hyperspheres.
problem The dataset lies on a low-dimensional submanifold in high-dimensional space.
method Constructing osculating hyperspheres and applying surgery theory to embed the hypersurface.
result The manifold hypothesis holds for embedding dimensionalities up to d − 1 d-1 d − 1 . Proves surface embedding theorem for 4-manifolds with good fundamental group.
problem Surface embedding in 4-manifolds with good fundamental group.
method Introduces dual spheres and Kervaire-Milnor invariant for computation.
result Combinatorial formula for Kervaire-Milnor invariant.
New constraints on embedded spheres and projective planes in 4-manifolds from Seiberg-Witten theory.
problem Constraints on configurations of embedded spheres and real projective planes in 4-manifolds.
method Equivariant Seiberg-Witten invariants and gluing formula for relative Seiberg-Witten invariants.
result Existence of certain configurations of surfaces leads to 4-manifolds of non-simple type.
Alternative proof of coisotropic embedding theorem for pre-symplectic manifolds.
problem Proving the coisotropic embedding theorem for pre-symplectic manifolds.
method Recast geometric choice of connection as algebraic embedding into cotangent bundle, identify symplectic thickening as submanifold of Hamiltonian momenta conjugate to kernel directions.
result Alternative proof of the coisotropic embedding theorem.
In this note, we discuss embeddings of 3 3 3 --manifolds via open books. First we show that every open book of every closed orientable 3 3 3 --manifold admits an open book embedding in any open book decompistion of S 2 × S 3 S^2 \times S^3 S 2 × S 3 and S 2 × ~ S 3 S^2 \widetilde{\times} S^3 S 2 × S 3 with the page a disk bundle over S 2 S^2 S 2 and monodromy the iden…
In this survey article we describe different ways of embedding fillings of contact 3-manifolds into closed symplectic 4-manifolds.
We show that, for a closed orientable n-manifold, with n not congruent to 3 modulo 4, the existence of a CR-regular embedding into complex (n-1)-space ensures the existence of a totally real embedding into complex n-space. This implies that a closed orientable (4k+1)-manifold with non-vanishing Kervaire semi-characteri…
Survey article on multibranched surfaces in 3-manifolds.
problem Embedding multibranched surfaces into 3-manifolds.
method Survey and review of existing methods.
result Overview of current research and techniques.
Paper shows graphs can be embedded in lower dimensions than expected.
problem Choosing the right embedding dimension for graph analysis.
method Utilizes hidden manifold structure to predict lower-dimensional embedding.
result Graphs can be embedded in much lower dimensions than previously thought.
New obstruction found for embedding Riemannian manifolds into Euclidean spaces.
problem Embedding Riemannian manifolds into Euclidean spaces with specific conditions.
method Motivated by incompressible Euler equations, a dynamical-topological obstruction is derived.
result Nontrivial first real homology and trivial center of fundamental group imply embedding violation.
This is a collection of notes on embedding problems for 3-manifolds. The main question explored is `which 3-manifolds embed smoothly in the 4-sphere?' The terrain of exploration is the Burton/Martelli/Matveev/Petronio census of triangulated prime closed 3-manifolds built from 11 or less tetrahedra. There are 13766 mani…
The study explores how 3-manifolds embed locally flatly in S 4 S^4 S 4 .
problem Embedding homology 3-spheres in S 4 S^4 S 4 locally flatly. method Survey of known results, focusing on Seifert fibred 3-manifolds and using 4-dimension surgery.
result Characterization of embeddings by properties of complementary regions.
Embeddings of surfaces in 5-manifolds are classified by an invariant.
problem Classifying isotopy classes of surface embeddings in 5-manifolds.
method Construction of an invariant defined in terms of homotopy groups.
result Isotopic embeddings of surfaces in 5-manifolds are classified by the invariant.
Let M be a compact Sasakian manifold. We show that M admits a CR-embedding into a Sasakian manifold diffeomorphic to a sphere, and this embedding is compatible with the respective Reeb fields. We argue that a stronger embedding theorem cannot be obtained. We use an extension theorem for Kaehler geometry: given a compac…
Study embedding of achiral Lefschetz fibrations in 6D manifolds.
problem Embedding achiral Lefschetz fibrations in 6D manifolds.
method Analyzing Lefschetz fibrations bounding open books and embedding them in 6D manifolds.
result Every achiral Lefschetz fibration with hyperelliptic monodromy admits LF embedding in D 6 = D 2 i m e s D 4 D^6 = D^2 imes D^4 D 6 = D 2 im es D 4 .