The paper extends Johnson homomorphisms to groups with extended N-series.
problem Johnson homomorphisms for mapping class groups.
method Developed a theory of Johnson homomorphisms for groups with extended N-series.
result Many known and new variants of Johnson homomorphisms.
Study various series of groups and their Lie algebras in split extensions.
problem Understanding different series of groups and their Lie algebras in split extensions.
method General construction of N-series, semi-direct products, and monodromy action.
result Generalize the well-known theorem of Falk-Randell to other versions of the LCS.
In the present article, we combine some techniques in the harmonic analysis together with the geometric approach given by modules over sheaves of rings of twisted differential operators (D-modules), and reformulate the composition series and branching problems for objects in the Bernstein-Gelfand-Gelfand pa…
New invariants for welded and extended welded knots found using multi-skein relations.
problem Classifying and distinguishing welded and extended welded knots and links.
method Developed a multi-skein relation approach to find invariants for these knots and links.
result Found sufficient conditions on coefficients for invariance under extended Reidemeister moves.
Paper proves Markov's theorem for extended welded braids and links.
problem Generalizing welded links to extended welded links and braids.
method Following Kamada's approach, proving Alexander and Markov's theorems for extended welded braids and links.
result Proves versions of Alexander and Markov's theorems for extended welded braids and links.
The paper studies lifts of complex structures on a manifold.
problem Understanding higher-order lifts of extended almost complex structures.
method Proved theorems on Nijenhuis tensor and introduced a new tensor field.
result Basic results on almost analytic complex vectors are investigated.
Automorphisms of surfaces extendable over 4-sphere with invariant spin structures.
problem Extendability of automorphisms of surfaces over the 4-sphere.
method Constructing invariant spin structures and embeddings.
result Each automorphism of a surface is extendable over the 4-sphere after a connected sum with a torus.
We define the category of manifolds with extended tangent bundles, we study their symmetries and we consider the analogue of equivariant cohomology for actions of Lie groups in this category. We show that when the action preserves the splitting of the extended tangent bundle, our definition of extended equivariant coho…
Study on extended weakly symmetric spaces, classifying and providing an example.
problem Understanding geometric properties of extended weakly symmetric spaces.
method Classification and presentation of a non-trivial example.
result Existence of extended weakly symmetric spaces established.
Extended Ville's inequality for nonintegrable supermartingales.
problem Nonintegrable nonnegative supermartingales.
method Derivation of extended Ville's inequality and extension of the method of mixtures.
result Strengthened classical Ville's inequality for nonintegrable settings.
The paper studies extended quasi-Einstein manifolds with special geometric properties and solitons.
problem Exploring new types of manifolds in general relativity.
method Generalization of existing manifolds and construction of specific examples.
result Existence and properties of extended quasi-Einstein manifolds with solitons.
Let Σg(g>1) be a closed surface embedded in S3. If a group G can acts on the pair (S3,Σg), then we call such a group action on Σg extendable over S3. In this paper we show that the maximum order of extendable cyclic group actions is 4g+4 when g is even and 4g−4 when g is odd; the maximum ord…
To give a Cartan calculus on the extended quantum 3d space, the noncommutative differential calculus on the extended quantum 3d space is extended by introducing inner derivations and Lie derivatives.
The paper studies mean curvature flow in a Ricci flow background with extended Ricci flow.
problem Analyzing mean curvature flow in a Ricci flow background.
method Computing variational properties and deriving evolution equations for mean curvature and second fundamental form.
result Established a Huisken's monotonicity-type formula for mean curvature solitons in an extended Ricci flow.
This paper provides a structural decomposition for extended function groups.
problem No existing literature states a structural decomposition for extended function groups.
method Uses the Klein-Maskit combination theorems.
result States and proves a structural decomposition for extended function groups.
Two elements generate extended mapping class groups of certain surfaces.
problem Generating extended mapping class groups with specific elements.
method Analyzing finite order elements and isotopy classes of homeomorphisms.
result Extended mapping class groups of certain surfaces are generated by two elements of finite order.
Classifies and constructs all extendable automorphisms of closed surfaces over the 3-sphere.
problem Identifying extendable automorphisms of closed surfaces over the 3-sphere.
method Classification and construction of extendable automorphisms through embeddings and Heegaard surfaces.
result All extendable automorphisms of closed surfaces can be induced by automorphisms of the 3-sphere on Heegaard surfaces.
No Einstein metrics found on extended graph 4-manifolds.
problem Finding Einstein metrics on extended graph 4-manifolds.
method Defined and analyzed extended graph 4-manifolds as per [FLS15].
result Extended graph 4-manifolds do not support Einstein metrics.
Automorphisms of a genus-2 surface extend over 3-sphere.
problem Extending automorphisms of a genus-2 surface over the 3-sphere.
method Classification of essential annuli in genus-2 handlebodies embedded in 3-sphere.
result An automorphism of a genus-2 surface extends to an automorphism of the pair (S^3, Σ) over the 3-sphere.
Let (V,(.,.)) be a pseudo-Euclidean vector space and S an irreducible Cl(V)-module. An extended translation algebra is a graded Lie algebra m = m_{-2}+m_{-1} = V+S with bracket given by ([s,t],v) = b(v.s,t) for some nondegenerate so(V)-invariant reflexive bilinear form b on S. An extended Poincaré structure on a manifo…
Extends Morse structures to partial open books for studying contact 3-manifolds.
problem Analyzing contact 3-manifolds with convex boundaries.
method Develops Morse structures on extendable partial open books.
result New tools for studying contact 3-manifolds with convex boundaries.
Extended mapping class groups can be generated by two elements for low genus cases.
problem Generating finite order elements to represent extended mapping class groups.
method Proving finite order generating sets for specific genus cases.
result Extended mapping class groups can be generated by two elements for genus 3 and 4, but not for genus 1.
Finite group actions on surfaces extend to 3-manifolds.
problem Classifying extendable periodic automorphisms of surfaces.
method Using fixed embeddings and 1-dominated 3-manifolds.
result All periodic automorphisms of closed surfaces extend to 3-spheres.
Study of extended Bianchi-Cartan-Vranceanu spaces in seven dimensions.
problem Understanding geometric properties of extended Bianchi-Cartan-Vranceanu spaces.
method Investigation of Levi-Civita connection, Ricci curvatures, Killing fields, and geodesics in seven-dimensional EBCV spaces.
result Characterization of geometric properties in extended Bianchi-Cartan-Vranceanu spaces.
Study extended Bogomolny equations on curved space with special boundary conditions.
problem Classify solutions to extended Bogomolny equations with gauge group SU(2).
method Relate solutions to holomorphic data via Kobayashi-Hitchin correspondence.
result Completely classify solutions to the extended Bogomolny equations.
Study on embeddings of surfaces in 4-manifolds and their mapping classes.
problem Characterizing and understanding embeddings of surfaces in 4-manifolds and their mapping classes.
method Analyzing smooth proper embeddings and mapping classes induced by diffeomorphisms of 4-manifolds.
result Most surfaces do not admit flexible embeddings in 4-manifolds with specific homology types.
Examples show cyclic actions on 4-manifolds can't extend to Hamiltonian circle actions.
problem Cyclic group actions on 4-manifolds that trivialize homology cannot be extended to Hamiltonian circle actions.
method Holomorphic methods applied to combinatorial tools for circle actions.
result Cyclic actions on 4-manifolds that trivialize homology do not extend to Hamiltonian circle actions.
Study utility maximization with costs, proving convergence and strategies.
problem Utility maximization with proportional transaction costs.
method Extended weak convergence theory and Meyer--Zheng topology.
result Prove convergence of utility maximization problems and optimal trading strategies.
Extended signatures help distinguish non-concordant links.
problem Distinguishing non-concordant links using signatures.
method Defined and studied an n-variable extension of the Levine-Tristram signature, proving it a concordance invariant on a dense subset of the torus.
result Found an infinite family of 3-component links not concordant to their mirror images, detectable only by the extended signature.
This paper describes dihedral extended Schottky groups and their symmetries.
problem Understanding symmetries of handlebodies with Schottky structures.
method Geometrical structural description of dihedral extended Schottky groups using Klein-Maskit combination theorems.
result Sharp upper bounds for the fixed points of symmetries in handlebodies.
In this paper, we introduce an equivalence relation on the set of local moves and classify local moves, called the extended ST-moves, up to the equivalence. Moreover, by inducing a binary relation on the set of equivalence classes of local moves, we show that an extended ST-move realizes the crossing change or the …
On a closed symplectic surface Sigma of genus two or more, we give a new construction of an extended flux map (a crossed homomorphism from the symplectomorphism group Symp(Sigma) to the cohomology group H^1(Sigma;R) that extends the flux homomorphism). This construction uses the topology of the Jacobian of the surface …
Classifies extended Abelian Chern-Simons theories using quadratic modules.
problem Classifying extended Abelian Chern-Simons theories.
method Using quadratic modules to classify theories.
result Finite quadratic modules classify extended Abelian Chern-Simons theories.
Study prices compound and extendible options using mixed fractional Brownian motion with jumps.
problem Pricing compound and extendible options under mixed fractional Brownian motion with jumps.
method Analytic formula derived under risk-neutral measure, applied to extendible options, discussed special cases, provided numerical results.
result An analytic formula for pricing compound options derived.
Extends Popularity Bias Memorization theorem to new conditions.
problem Estimating alignment with top-k singular hyperspace.
method Extending theorem to arbitrary degree distributions and proving upper and lower bounds.
result Upper and lower estimates for alignment with top-k singular hyperspace.
Extended Kalman Filter is shown to be a gradient descent in trajectory space.
problem Estimating state of dynamical systems from noisy measurements.
method Recovery of extended Kalman filter equations from Amari's natural gradient in trajectory space.
result Extended Kalman Filter is equivalent to natural gradient descent in trajectory space.
We present the extended Kuranishi space for Kodaira surface as a non-trivial example to Kontsevich and Barannikov's extended deformation theory. We provide a non-trivial example of Hertling-Manin's weak Frobenius manifold. In addition, we find that Kodaira surface is its own mirror image. Our computation is done in the…
Extended Riemannian geometry aids in DFT formulations.
problem Describing current DFT formulations with clarity.
method Using graded manifolds and extended symmetries.
result Covariant strong section condition and global descriptions.
This is primarily a survey of the developments in the theory of harmonic maps of finite uniton number (or unitons) which have taken place since the introduction of extended solutions by Uhlenbeck. Such maps include all harmonic maps from the two-sphere to a compact Lie group or symmetric space. Extended solutions are e…
The paper studies geometric constants under modified Ricci flows with variable parameters.
problem Understanding geometric constants under variable coupling parameters in Ricci flows.
method Introduced modified Ricci flows with variable coefficients, derived evolution formulas, and proved monotonicity conditions.
result Conditions for maintaining monotonicity of geometric constants under modified Ricci flows.
Torsion elements on surfaces extend over 4-sphere in various ways.
problem Extending torsion elements of mapping class groups over 4-sphere.
method Analyzing different types of embeddings and orders of torsion elements.
result Conditions for extendability of torsion elements over 4-sphere.
Study shows cohomological limits on extending actions on 3-manifold boundaries.
problem Limits to extending group actions on 3-manifold boundaries.
method Cohomological obstructions for C0-actions on 3-manifolds. result Cohomological obstructions prevent extending actions on certain 3-manifold boundaries.
Goosen extends TQFTs using generators and relations for a simple example.
problem Developing a formalism for 3D TQFTs with generators and relations.
method Combining string-net and generators-and-relations formalisms for a specific example.
result Provides an elementary string-net description of linear maps and mapping class group action.
Deep neural network model extends matrix completion to unseen data.
problem Limited extendability of neural-network-based matrix completion models.
method Two-branch neural network model that can predict and extend to unseen data.
result Model outperforms state-of-the-art in accuracy and extendability.
New findings on pseudo-Anosov maps extending powers to 3-manifold interiors.
problem Understanding when and how pseudo-Anosov maps can extend to the interior of 3-manifolds.
method Constructed a family of pseudo-Anosov maps and 3-manifolds to demonstrate non-universal power bounds.
result Power required for pseudo-Anosov maps to extend is not universally bounded.
Defines extended TQFTs using handle attachments.
problem Constructing extended topological quantum field theories (TQFTs).
method Finite presentation of cobordism symmetric monoidal bicategory using handle attachments and relations.
result Constructs a once extended TQFT from categorified TQFT and handle 2-morphisms.
New method classifies immersed surfaces extending from circles in surfaces.
problem Classifying immersed surfaces extending from circles in surfaces.
method New straightforward method for determining topological equivalence classes.
result Determines all topological equivalence classes of immersed surfaces.
Extends h-principle to stratified spaces using sheaf and jet theories.
problem Applying h-principle to stratified spaces.
method Developed new sheaf and bundle theories for stratified spaces, and proved the h-principle.
result Stratified continuous sheaves and homotopy fiber sheaves lead to the parametric h-principle.