New proof using Heegaard Floer theory for non-extendable twists.
problem Non-extendable twists in 4-manifolds with group actions.
method Heegaard Floer homology approach.
result Different proof of Auckly-Kim-Melvin-Ruberman's phenomenon.
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48 results for “non-extendable twists”
Paper proves non-extendability of quasimorphism and non-vanishing of Reznikov's class.
problem Non-extendability of Shelukhin's quasimorphism and non-vanishing of Reznikov's class.
method Analyzing specific symplectic manifolds like blow-ups of tori and products of surfaces.
result Non-extendability of Shelukhin's quasimorphism and non-vanishing of Reznikov's class for certain symplectic manifolds.
The study examines spaces of non-extendable quasimorphisms for group pairs.
problem Analyzing the space of non-extendable quasimorphisms for group pairs.
method Established a five-term exact sequence of cohomology relative to bounded subcomplex.
result Proved stable commutator length equivalent to stable mixed commutator length for certain pairs.
Extends Killing vector fields in electrovacuum spacetimes, proving non-extendibility.
problem Extension of Killing vector fields in electrovacuum spacetimes.
method Inspired by Ionescu-Klainerman's technique for Ricci flat manifolds, extends to strong null convex domains.
result Shows non-extendibility of Hawking vector field in Kerr-Newman solutions near horizons.
The paper studies quasimorphisms on groups and proves non-existence results for symplectic geometry.
problem Non-existence of sections of flux homomorphisms on higher genus surfaces.
method Analysis of -invariant quasimorphisms and symplectic geometry of surfaces.
result Py's Calabi quasimorphism is the unique non-extendable quasimorphism to some group.
New result on symplectomorphisms on surfaces, showing vanishing cup product of fluxes.
problem Understanding commuting symplectomorphisms on surfaces.
method Refinement of non-extendability result for Py's Calabi quasimorphism.
result Vanishing cup product of fluxes for commuting symplectomorphisms.
Study symplectic and Hamiltonian actions on irrational ruled surfaces, proving existence and non-existence of extensions.
problem Tackles the extension of symplectic and Hamiltonian cyclic actions to Hamiltonian circle actions on irrational ruled symplectic 4-manifolds.
method Constructs symplectic involutions and cyclic actions, classifies symplectic morphisms, and proves non-extendability of certain actions.
result Shows existence and non-existence of Hamiltonian circle actions for different cyclic actions on irrational ruled symplectic 4-manifolds.
Survey on invariant quasimorphisms and their relation to stable commutator length.
problem Understanding the relationship between invariant quasimorphisms and stable commutator length.
method Review of existing methods and examples in invariant quasimorphisms and their relation to stable commutator length.
result The existence of non-extendable invariant quasimorphisms is closely related to the behavior of stable mixed commutator length.
Example of group action on surface that can't extend to 3-manifold.
problem Finding group actions on surfaces that can't be extended to 3-manifolds.
method Provided a first known example and sufficient conditions for infinitely many such actions.
result Finite group actions on surfaces that are free and orientation-preserving do not extend to arbitrary actions on 3-manifolds.
Unified proof of four Bavard dualities and new results on quasimorphisms.
problem Comparing stable commutator length and quasimorphisms on groups.
method Expository account and new strengthening of Bavard duality, providing complete proofs.
result Generalized mixed Bavard duality, recovering all previous dualities.
New invariants detect corks obstructing homology ball extensions.
problem Detecting corks obstructing homology ball extensions.
method Adapting Heegaard Floer homology formalism for local equivalence, using monotonicity and surgery.
result Established new families of corks and proved various examples are strongly non-extendable.
Researchers provide a simple topological method for Burau representations of loop braid groups.
problem Constructing Burau representations of loop braid groups.
method Simple topological construction of the Burau representations.
result One of the representations is more subtle and topologically natural but not easily combinatorially obvious.
New findings on plane waves in 3D spacetimes, showing non-unimodular elliptic plane waves are unique.
problem Classifying Lorentz homogeneous spaces of dimension 3, focusing on plane waves.
method Revisiting and relaxing usual completeness assumptions, characterizing homogeneous plane waves.
result Non-unimodular elliptic plane waves are unique and non-extendable, geodesically complete only if symmetric.
A complex structure on a subset of S^6 cannot be extended to a global integrable structure.
problem Non-integrability of complex structures on subsets of S^6.
method Proving the non-integrability of extensions of a specific complex structure on a subset of S^6.
result It is impossible to deform a non-integrable structure to an integrable one on S^6 while fixing it on a subset.
The study proves conditions for symplectic torus actions on manifolds with non-contractible orbits.
problem Conditions for symplectic torus actions with non-contractible orbits.
method Analyzes symplectic torus actions on manifolds, proving conditions for Hamiltonian actions and orbit properties.
result Symplectic actions with non-contractible orbits are not Hamiltonian unless the orbits are contractible.
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.
New theory classifies knotted spheres in 4D space.
problem Classifying knotted punctured spheres in 4D space.
method Diagrammatic theory of welded graphs, Tube map extension, Milnor invariants.
result Complete link-homotopy classification of knotted punctured spheres.
Unified framework for solving linear systems with improved convergence rates.
problem Efficiently solving linear systems with randomized batch-sampling methods.
method Developed a unified randomized batch-sampling Kaczmarz framework with concentration inequalities for analysis.
result Derived new expected linear convergence rate bounds that are tighter and more reflective of empirical behavior.
By using a Borel density theorem for algebraic quotients, we prove a theorem concerning isometric actions of a Lie group on a smooth or analytic manifold with a rigid -structure . It generalizes Gromov's centralizer and representation theorems to the case where is split solvable and $G/R(G…
We introduce the concept of twisted contact groupoids, as an extension either of contact groupoids or of twisted symplectic ones, and we discuss the integration of twisted Jacobi manifolds by twisted contact groupoids. We also investigate the very close relationships which link homogeneous twisted Poisson manifolds wit…
New infinite families of twisted torus knots found.
problem Identifying new types of twisted torus knots.
method Finding new infinite families of twisted torus knots with a single negative twist.
result Eight new infinite families of twisted torus knots are discovered.
The study finds hyperbolic twisted torus links for certain twists.
problem Identifying hyperbolic twisted torus links.
method Analyzing -torus links with strands twisted times.
result All hyperbolic twisted torus links are identified for .
Twisted submanifolds of R^nmath-ph
The paper introduces a method to deform submanifolds in Euclidean space using Drinfel'd twists.
problem Constructing noncommutative deformations of submanifolds in Euclidean space.
method Using Drinfel'd twist deformation of differential geometry, the paper proposes a general procedure to construct noncommutative deformations of an embedded submanifold.
result The method allows for consistent projection of connections and can be applied to various submanifolds like cylinders and hyperboloids.
Paper constructs Chern character for higher twists and shows isomorphism between K-theory and cohomology.
problem Mapping higher twisted K-theory to higher twisted cohomology.
method Constructing Chern character for higher twists and showing isomorphism.
result Chern character gives isomorphism between higher twisted K-theory and higher twisted cohomology.
Paper finds a minimal set of Dehn twists to generate twist subgroup of non-orientable surfaces.
problem Finding a minimal set of Dehn twists to generate the twist subgroup of non-orientable surfaces.
method Used Dehn twists and an argument from Hirose [5] to find a minimal generating set.
result Found a generating set with one less element than the lower bound.
New algebraic structure for distinguishing twisted virtual handlebody-links.
problem Distinguishing twisted virtual handlebody-links.
method Introducing twisted virtual bikeigebras and using them to define invariants.
result New invariants distinguish some twisted virtual handlebody-links.
The paper studies Gluck twists on 2-knots with periodic monodromy.
problem Determining the resulting 2-knot after a Gluck twist on a 2-knot with periodic monodromy.
method Analyzes the Gluck twist on branched twist spins of 2-knots.
result Provides infinitely many pairs of inequivalent branched twist spins with homeomorphic complements.
Construct noncommutative deformations of algebraic submanifolds in R^n.
problem Deforming algebraic submanifolds in noncommutative geometry.
method Using twisted differential geometry and Drinfel'd twists, constructing noncommutative deformations of algebraic submanifolds.
result Explicitly worked out deformations of quadrics in R^3.
The paper studies the twisted Calabi flow on Kähler manifolds.
problem Analyzing the behavior of the twisted Calabi flow on compact Kähler manifolds.
method Establishing convexity, proving short-time existence, and demonstrating stability of the flow.
result The stability of the twisted Calabi flow near twisted constant scalar curvature Kähler metrics.
Twisted braidsmath.GT
Paper proves any twisted link can be described as a unique twisted braid.
problem Understanding twisted links and braids.
method Proved using Alexander and Markov Theorems for classical braids and links.
result Any twisted link can be described as the closure of a unique twisted braid.
Study on singular twisted links and virtual braids, extending knot theory concepts.
problem Extending knot theory concepts to singular twisted links and virtual braids.
method Definition and analysis of singular twisted virtual braids and their monoid structure.
result Presentation of monoid and reduced monoid for singular twisted virtual braids.
In this paper, we develop differential twisted K-theory and define a twisted Chern character on twisted K-theory which depends on a choice of connection and curving on the twisting gerbe. We also establish the general Riemann-Roch theorem in twisted K-theory and find some applications in the study of twisted K-theory o…
Proves existence of Kähler-Einstein metrics with certain twisting forms.
problem Existence of Kähler-Einstein metrics under stability conditions.
method Proves existence assuming twisted K-stability condition, allows certain non-negative twisting forms.
result Existence of twisted Kähler-Einstein metrics under specified conditions.
The paper extends knot theory to twisted virtual braids and links.
problem Generalizing knot theory to include twists.
method Introduced twisted virtual braids and proved theorems for twisted links.
result The Alexander and Markov theorems were extended to twisted links.
Twisting cubic rabbitsmath.DS
Solves infinite family of cubic polynomial problems.
problem Infinite family of twisted polynomial problems.
method Using Dehn twists and 9-adic expansions.
result Result of twisting depends on 9-adic expansion.
The paper introduces colorings and invariants for twisted links and shows how double coverings can be equivalent.
problem Understanding and distinguishing twisted links.
method Twisted intersection colorings and double coverings.
result There exist infinitely many pairs of twisted links with equivalent double coverings.
This is the first in a series of papers constructing geometric models of twisted differential K-theory. In this paper we construct a model of even twisted differential K-theory when the underlying topological twist represents a torsion class. By differential twists we will mean smooth U(1)-gerbes with connection, and w…
We study twisted Jacobi manifolds, a concept that we had introduced in a previous Note. Twisted Jacobi manifolds can be characterized using twisted Dirac-Jacobi, which are sub-bundles of Courant-Jacobi algebroids. We show that each twisted Jacobi manifold has an associated Lie algebroid with a 1-cocycle. We introduce t…
A virtual link can be understood as a link in a trivial I-bundle over an orientable compact surface with genus. A twisted virtual link is a link in a trivial I-bundle over a not-necessarily orientable compact surface. A twisted virtual birack is an algebraic structure with axioms derived from the twisted virtual Reidem…
Field theories help describe twisted bundles on orbifolds.
problem Understanding twisted cohomology and vector bundles on orbifolds.
method Construction of twist functor for 1|1-dimensional EFTs from gerbe data.
result Construction of supersymmetric field theories from twisted vector bundles.
Null-homologous unknottingsmath.GT
Knots can be unknotted with specific twists, proving bounds on the number of twists needed.
problem The minimum number of twists needed to unknock a knot of a given genus.
method Proved using null-homologous twists, showing bounds on the number of twists required.
result There exist knots of genus g that cannot be unknotted with fewer than 2g null-homologous twists.
Formula for Alexander polynomial of twisted torus knots derived.
problem Calculating Alexander polynomial for a specific class of knots.
method Knot group presentation combined with Fox's calculus.
result Explicit formula for Alexander polynomial of twisted torus knots.
New families of twisted torus knots found with essential surfaces.
problem Whether all twisted torus knots have essential tori.
method Analyzing sequences of twists on torus knots.
result Found two new families of toroidal twisted torus knots.
Characterizes a specific type of spacetime using vector fields.
problem Classifying a specific type of spacetime.
method Using vector fields to characterize 1+n doubly twisted spacetimes.
result Simple classification of 1+n doubly-twisted spacetimes.
New examples of positive twisted torus knots with same surface slope found.
problem Finding new examples of positive twisted torus knots with same surface slope.
method Extending Dean's conditions and using new four-parameter family.
result Four-parameter family of positive twisted torus knots with same surface slope.
Introduces a new periodic Deligne cohomology with twists by gerbes.
problem Extending Deligne cohomology to higher degrees and periodic forms.
method Combining periodic integral cohomology and Rham complex twists.
result Demonstrates the existence of a twist by gerbes of any odd degree.
Study lattice paths from twist knots and double twist knots.
problem Understanding combinatorics of twist knots and double twist knots.
method Analyzing quiver generating series of HOMFLY-PT polynomial limits.
result Lattice path models for twist knots and double twist knots.
Paper studies involutions generating the twist subgroup of nonorientable surfaces.
problem Generating the twist subgroup by involutions on nonorientable surfaces.
method Analyzes involutions to find the smallest generating sets.
result Provides generating sets of involutions with minimal elements.