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.
Solves generalized twisted rabbit problems for higher degree polynomials.
Solves infinite family of cubic polynomial problems.
We give a simple algorithm that determines whether a given post-critically finite topological polynomial is Thurston equivalent to a polynomial. If it is, the algorithm produces the Hubbard tree; otherwise, the algorithm produces the canonical obstruction. Our approach is rooted in geometric group theory, using iterati…
In recent years, deep reinforcement learning has been shown to be adept at solving sequential decision processes with high-dimensional state spaces such as in the Atari games. Many reinforcement learning problems, however, involve high-dimensional discrete action spaces as well as high-dimensional state spaces. This pa…
Study inverse problems for twisted geodesic flows on manifolds.
A generalization of the Euler-Plateau problem to account for the energy contribution due to twisting of the bounding loop is proposed. Euler-Lagrange equations are derived in a parameterized setting and a bifurcation analysis is performed. A pair of dimensionless parameters govern bifurcations from a flat, circular gro…
Study on realizing subgroup twists in 3-manifolds.
Study improves recognition of long-tail visual relationships.
According to an analogy to quasi-Fuchsian groups, we investigate topological and combinatorial structures of Lyubich and Minsky's affine and hyperbolic 3-laminations associated with the hyperbolic and parabolic quadratic maps. We begin by showing that hyperbolic rational maps in the same hyperbolic component have quasi…
Let Gamma be a group generated by two positive multi-twists. We give some sufficient conditions for Gamma to be free or have no `unexpectedly reducible' elements. For a group Gamma generated by two Dehn twists, we classify the elements in Gamma which are multi-twists. As a consequence we are able to list all the lanter…
Geometrically interpolates rigid body motions with initial and terminal twists.
Study of Dehn twists on a disc with 3 points, solving conjugacy problem.
Study shows Dehn twists on certain 4-manifolds cannot be realized by finite order diffeomorphisms.
New relation found in 4D symplectic mapping class group.
We study the geometric quantization process for twisted Poisson manifolds. First, we introduce the notion of Lichnerowicz-twisted Poisson cohomology for twisted Poisson manifolds and we use it in order to characterize their prequantization bundles and to establish their prequantization condition. Next, we introduce a p…
We give a short introduction to the theory of twisted Alexander polynomials of a 3--manifold associated to a representation of its fundamental group. We summarize their formal properties and we explain their relationship to twisted Reidemeister torsion. We then give a survey of the many applications of twisted invarian…
Dehn twists on K3-type 4-manifolds are not homotopy coherently Nielsen realizable.
The twisting number of a ribbon knot is at least as large as its doubly slice genus.
We define symplectic fractional twists, which generalize Dehn twists, and use these in open books to investigate contact structures. The resulting contact structures are invariant under a circle action, and share several similarities with the invariant contact structures that were studied by Lutz and Giroux. We show th…
Study representation varieties of twisted Hopf links using combinatorial and Hodge theory.
In the background effective field theory of heterotic string theory, the Green-Schwarz anomaly cancellation mechanism plays a key role. Here we reinterpret it and its magnetic dual version in terms of differential twisted String- and differential twisted Fivebrane-structures that generalize the notion of Spin-structure…
In this paper we give an algorithm for solving a main case of the conjugacy problem in the braid groups. We also prove that half-twists satisfy a special root property which allows us to reduce the solution for the conjugacy problem in half-twists into the free group. Using this algorithm one is able to check conjugacy…
Proves bounds on ribbonlength for various knot types.
Self-distillation improves constrained language generation by aligning models with target distributions.
We give a survey of some recent papers by the authors and Masaaki Wada relating the twisted Alexander polynomial with a partial order on the set of prime knots. We also give examples and pose open problems.
Study shows non-spin 4-manifolds where smooth Nielsen realization fails.
We begin the systematic study of knot polynomials for the twist satellites of a knot, when its strand is substituted by a 2-strand twist knot. This is a generalization of cabling (torus satellites), when the substitute of the strand was a torus knot. We describe a general decomposition of satellite's colored HOMFLY in …
The twisted face-pairing construction of our earlier papers gives an efficient way of generating, mechanically and with little effort, myriads of relatively simple face-pairing descriptions of interesting closed 3-manifolds. The corresponding description in terms of surgery, or Dehn-filling, reveals the twist construct…
We prove that two angle-compatible Coxeter generating sets of a given finitely generated Coxeter group are conjugate provided one of them does not admit any elementary twist. This confirms a basic case of a general conjecture which describes a potential solution to the isomorphism problem for Coxeter groups.
In this paper we apply the twisted Alexander polynomial to study the fibering and genus detecting problems for oriented links. In particular we generalize a conjecture of Dunfield, Friedl and Jackson on the torsion polynomial of hyperbolic knots to hyperbolic links, and confirm it for an infinite family of hyperbolic 2…
We provide a systematic approach to describing the Ramond-Ramond (RR) fields as elements in twisted differential K-theory. This builds on a series of constructions by the authors on geometric and computational aspects of twisted differential K-theory, which to a large extent were originally motivated by this problem. I…
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…
Noninvasive MR-guided focused ultrasound (MRgFUS) treatments are promising alternatives to the surgical removal of malignant tumors. A significant challenge is assessing the viability of treated tissue during and immediately after MRgFUS procedures. Current clinical assessment uses the nonperfused volume (NPV) biomarke…
New infinite families of twisted torus knots found.
The study finds hyperbolic twisted torus links for certain twists.
The paper introduces a method to deform submanifolds in Euclidean space using Drinfel'd twists.
Paper constructs Chern character for higher twists and shows isomorphism between K-theory and cohomology.
Margalit and Schleimer observed that Dehn twists on orientable surfaces have nontrivial roots. We investigate the problem of roots of a Dehn twist t_c about a nonseparating circle c in the mapping class group M(N_g) of a nonorientable surface N_g of genus g. We explore the existence of roots and, following the work of …
The paper studies the twisted Calabi flow on Kähler manifolds.
Construct noncommutative deformations of algebraic submanifolds in R^n.
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…
Study on singular twisted links and virtual braids, extending knot theory concepts.
Paper proves any twisted link can be described as a unique twisted braid.
We use SMC with twist functions to improve probabilistic inference in LLMs.
The paper extends knot theory to twisted virtual braids and links.
The paper introduces colorings and invariants for twisted links and shows how double coverings can be equivalent.
Study of spacelike hypersurfaces in twisted product spacetimes with specific conditions.
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…