Classifies 3-braid knots with maximal 4-genus using McCoy's method.
problem Classifying 3-braid knots with maximal 4-genus.
method McCoy's twisting method and Xu normal form.
result Upper bounds for the topological 4-genus of 3-braid knots.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,051 papers · 148 categories
Trend · papers per month
48 results for “McCoy's twisting method”
Sharp signature bound for 3-strand torus knots proved.
problem Determining the topological 4-genus of 3-strand torus knots.
method Using McCoy's twisting method and improving upper bounds.
result Signature bound is sharp for 3-strand knots and off by at most 1 for 4- and 6-strand knots.
Proves conditions for odd pretzel knots to be doubly slice.
problem Identifying conditions for odd pretzel knots to be doubly slice.
method Analyzes knots with specific twist parameters and odd integers.
result Identifies all doubly slice odd pretzel knots.
We prove a complete family of `cylindrical estimates' for solutions of a class of fully non-linear curvature flows, generalising the cylindrical estimate of Huisken-Sinestrari for the mean curvature flow. More precisely, we show that, for the class of flows considered, an -convex () solution bec…
In this paper, we consider the mean curvature flow of convex hypersurfaces in Euclidean spaces with a general forcing term. We show that the flow may shrink to a point in finite time if the forcing term is small, or exist for all times and expand to infinity if the forcing term is large enough. The flow can also conver…
Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvaturemath.DG
We prove convergence results for expanding curvature flows in the Euclidean and hyperbolic space. The flow speeds have the form , where and is a positive, strictly monotone and 1-homogeneous curvature function. In particular this class includes the mean curvature . We prove that a certain initial…
New research shows that many slopes are characterizing for satellite knots.
problem Characterizing slopes for satellite knots.
method Detailed examination of the JSJ decomposition of a surgery along a knot, combined with other authors' constraints on surgery slopes.
result Many non-integral slopes are characterizing for composite knots.
This paper explores how many positive integer surgeries on a knot produce a manifold rational homology cobordant to a lens space.
problem How many positive integer surgeries on a knot produce a manifold rational homology cobordant to a lens space?
method Uses Greene and McCoy's changemaker lattices from Heegaard Floer d-invariants and Aceto-Celoria-Park's rational cobordisms and integral homology.
result For a given knot, there are at most two positive integer surgeries that produce a manifold rational homology cobordant to a lens space.
This paper concerns the evolution of a closed hypersurface of dimension in the Euclidean space under a mixed volume preserving flow. The speed equals a power of homogeneous, either convex or concave, curvature functions of degree one plus a mixed volume preserving term, incl…
The paper explores methods to decompose periodic maps into Dehn twists.
problem Factoring periodic maps into Dehn twists.
method Various methods for factoring periodic mapping classes into Dehn twists, up to conjugacy.
result Existence of conjugates of periodic maps whose product is pseudo-Anosov.
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.
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…
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.
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.
Formula for twisted orbital integrals using hypoelliptic Laplacian.
problem Evaluate equivariant trace of Laplacians on compact locally symmetric spaces.
method Using the hypoelliptic Laplacian method and twisted trace formula.
result Explicit geometric formula for twisted orbital integrals.
Study on realizing subgroup twists in 3-manifolds.
problem Realizing subgroups of twist groups in 3-manifolds.
method Analyzing Nielsen realization problem for Twist(M) subgroups, applying to Burnside problem.
result Nontrivial subgroups of Twist(M) are realized by diffeomorphisms if and only if they are cyclic and M is a connected sum of lens spaces.
New triangulations for twist knots, proving volume conjecture.
problem Computing the volume of twist knot complements.
method Ideal triangulations and H-triangulations, using Thurston's method and volume functional.
result Proved the Teichmüller TQFT volume conjecture for all twist knots.
Study on quantum invariants of twist knots using saddle point method.
problem Asymptotic expansion of Reshetikhin-Turaev invariants of twist knots.
method Saddle point method applied to integral -surgery.
result Asymptotic expansion formula for Reshetikhin-Turaev invariants.
Standard trisection diagrams found for a specific type of knot.
problem Finding standard trisection diagrams for Gluck twists.
method Using a specific method to obtain trisection diagrams for spun -torus knots.
result Standard trisection diagrams were found for the spun -torus knots.
Study on stable vector bundles over Gauduchon manifolds.
problem Existence and stability of vector bundles over Gauduchon manifolds.
method Uhlenbeck--Yau's continuity method for approximate Hermitian--Einstein structures.
result Equivalence of semi-stability and existence of Hermitian--Einstein structures.
New method to untangle knots using null-homologous twists.
problem Finding the minimum number of twists to convert a knot to the unknot.
method Using null-homologous twists as a generalization of crossing changes.
result The untwisting number is at most twice the surgery description number plus 1.
New method distinguishes knots and knotted surfaces.
problem Distinguishing knots and knotted surfaces.
method Twisted set-theoretic Yang-Baxter solutions and Alexander numbering.
result Distinguished -twist spun trefoil from its reverse.
Study on quantum invariants of twist knots at specific roots of unity.
problem Asymptotic expansions of quantum invariants for twist knots.
method Saddle point method applied to colored Jones polynomial.
result Asymptotic expansion formula for twist knots at given root of unity.
New Witten rigidity theorems for elliptic genus in various dimensions.
problem Proving rigidity theorems for elliptic genus in different dimensions.
method Combining Liu's and Han-Yu's methods to prove Witten rigidity theorems for elliptic genus in even and odd dimensions.
result Several new Witten rigidity theorems for elliptic genus in even and odd dimensions have been established.
New cohomology vanishing result for twisted cylinders.
problem Cohomology of twisted cylinders.
method Sobolev--Poincaré inequality methods.
result Vanishing result for -cohomology.
New rigidity theorems for spin^c manifolds using modular invariance.
problem Establishing rigidity theorems for twisted Dirac and Toeplitz operators.
method Liu's modular invariance method and its odd-dimensional extension.
result New Witten rigidity theorems for even and odd-dimensional spin^c manifolds.
The paper extends affine connection results to singular warped and twisted products.
problem Generalizing affine connections to singular warped and twisted products.
method Study of singular multiply warped products and singular twisted products with semi-symmetric metric and non-metric connections, discussing Koszul forms and curvature.
result Theoretical results on curvature and Koszul forms for singular multiply warped and twisted products.
In recent years, twisted Alexander polynomial has been playing an important role in low-dimensional topology. For Montesinos links, we develop an efficient method to compute the twisted Alexander polynomial associated to any linear representation. In particular, formulas for multi-variable Alexander polynomials of thes…
New method calculates number of components in twisted torus links.
problem Determining the number of components of twisted torus links.
method Euclidean algorithm-like procedure based on parameters.
result Number of components is a multiple of gcd(p, q, r, s).
Study of twisted Calabi flow connecting J-flow and Calabi flow on Kähler manifolds.
problem Existence and convergence of twisted Calabi flow on compact Kähler manifolds.
method Analysis of a family of twisted Calabi flows connecting J-flow and Calabi flow, showing long-time existence and convergence to cscK metrics.
result Long-time existence and convergence of twisted Calabi flow to cscK metrics, implying openness of continuity method.
The paper constructs triangulations for double twist knots using geometric methods.
problem Constructing explicit triangulations of double twist knots.
method Using triangulating Dehn fillings, layered solid tori, and their double covers.
result Proves both triangulations are geometric, using conjecturally minimal triangulation to present A-polynomial equations.
Unified framework designs LK structures using integer twists on non-manifold meshes.
problem Binary twisting limits topological possibilities and structural behaviors.
method Generalizes twist formulation to arbitrary integer labels for non-manifold meshes.
result Integer twists enable full connectivity and dynamic folding/articulation.
Highly twisted diagramsmath.GT
New proof shows certain knots are hyperbolic.
problem Characterizing knots with highly twisted diagrams.
method New approach involving Euler characteristic argument.
result Complements of certain knots are unannular and atoroidal.
Method constructs G2-instantons over twisted connected sums.
problem Constructing G2-instantons over complex manifolds.
method Gluing G2-instantons from holomorphic bundles over building blocks.
result Explicit examples from semi-Fano 3-folds.
In 1965, E. C. Zeeman proved that the (+/-)-twist spin of any knotted sphere in (n-1)-space is unknotted in the n-sphere. In 1991, Y. Marumoto and Y. Nakanishi gave an alternate proof of Zeeman's theorem by using the moving picture method. In this paper, we define a knotted 2-dimensional foam which is a generalization …
Improves inference-time alignment for diffusion models without updating weights.
problem Aligning diffusion models without updating weights for high-reward outputs.
method Trust-Region Iterative Twisted Sequential Monte Carlo (TRI-TSMC) for variance reduction and efficiency.
result Improves primary alignment objectives on text generation tasks.
Deep neural networks help recover two signals from noisy mixtures.
problem Recovering two signals from noisy subgaussian mixtures with prior structural information.
method Used deep generative neural networks (GNNs) to solve the demixing problem for Lipschitz signals.
result Proved a sample complexity bound for nearly optimal recovery error, extending previous results.
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.
In this paper we study a proposal of Nekrasov, Rosly and Shatashvili that describes the effective twisted superpotential obtained from a class S theory geometrically as a generating function in terms of certain complexified length-twist coordinates, and extend it to higher rank. First, we introduce a higher rank analog…
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 .
We use SMC with twist functions to improve probabilistic inference in LLMs.
problem Improving probabilistic inference in large language models.
method We use Sequential Monte Carlo with learned twist functions to estimate expected future values and focus inference on promising sequences.
result Twisted SMC improves the accuracy of language model inference and evaluation.
We give uniform, explicit, and simple face-pairing descriptions of all the branched cyclic covers of the 3-sphere, branched over two-bridge knots. Our method is to use the bi-twisted face-pairing constructions of Cannon, Floyd, and Parry; these examples show that the bi-twist construction is often efficient and natural…
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.
We introduce a notion of the twist of an isometry of the hyperbolic plane. This twist function is defined on the universal covering group of orientation-preserving isometries of the hyperbolic plane, at each point in the plane. We relate this function to a function defined by Milnor and generalised by Wood. We deduce v…
Explicit matrix presentations of Blanchfield pairings and twisted pairings for torus knots.
problem Computing explicit matrix presentations of Blanchfield and twisted Blanchfield pairings for torus knots.
method Using a taut identity to construct a chain complex with few generators, and describing the twisted Alexander module.
result Explicit matrix presentations of the Blanchfield pairing and twisted pairings for -torus knots.
Twisted Alexander invariants of knots are well-defined up to multiplication of units. We get rid of this multiplicative ambiguity via a combinatorial method and define normalized twisted Alexander invariants. We then show that the invariants coincide with sign-determined Reidemeister torsion in a normalized setting, an…
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.