arXiv research

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.

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.

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.

The paper extends knot theory to twisted virtual braids and links.

Solves infinite family of cubic polynomial problems.

The paper introduces colorings and invariants for twisted links and shows how double coverings can be equivalent.

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…

We generalize unoriented handlebody-links to the twisted virtual case, obtaining Reidemeister moves for handlebody-links in ambient spaces of the form $Σ\times [0,1]$ for $Σ$ a compact closed 2-manifold up to stable equivalence. We introduce a related algebraic structure known as twisted virtual bikeigebras whose axiom…

Characterizes a specific type of spacetime using vector fields.

New families of twisted torus knots found with essential surfaces.

Formula for Alexander polynomial of twisted torus knots derived.

Study lattice paths from twist knots and double twist knots.

The paper classifies twisted torus links that are unlinks.

Constructs differential models for twisted Spin^c-bordism and its dual, defining a new anomaly map.

Paper shows how to twist knots to make them trivial or non-trivial.

The paper uses Floer homology to study twist coefficients and their behavior after capping off.

We study the characteristic foliation of a twisted Jacobi manifold. We show that a twisted Jacobi manifold is foliated into leaves that are, according to the parity of the dimension, endowed with a twisted contact or a twisted locally conformal symplectic structure.

A twisted torus knot is a knot obtained from a torus knot by twisting adjacent strands by full twists. The twisted torus knots lie in $F$, the genus 2 Heegaard surface for $S^3$. Primitive/primitive and primitive/Seifert knots lie in $F$ in a particular way. Dean gives sufficient conditions for the parameters of the tw…

The union of singular orbits of an effective locally smooth circle action on the 4-sphere consists of two 2-knots, $K$ and $K^{\prime}$, intersecting at two points transversely. Each of $K$ and $K^{\prime}$ is called a branched twist spin. A twist spun knot is an example of a branched twist spin. The Gluck twists along…

The article examines twisted cohomologies on algebraic and analytic varieties.

The paper classifies hyperbolic and satellite T-links formed by twisting.

Lee's work on twisted torus knots with Fibonacci parameters is extended to Horadam parameters.

In this paper, we develop twisted $K$-theory for stacks, where the twisted class is given by an $S^1$-gerbe over the stack. General properties, including the Mayer-Vietoris property, Bott periodicity, and the product structure $K^i_α\otimes K^j_β\to K^{i+j}_{α+β}$ are derived. Our approach provides a uniform framework …

Satellite links with many twists have simpler companions.

We prove an existence result for twisted Kähler-Einstein metrics, assuming an appropriate twisted K-stability condition. An improvement over earlier results is that certain non-negative twisting forms are allowed.

Gluck twisting certain knots results in standard 4-spheres.

We give a small generating set for the twist subgroup of the mapping class group of a non-orientable surface by Dehn twists. The difference between the number of the generators and a lower bound of numbers of generators for the twist subgroup by Dehn twists is one. The lower bounds is obtained from an argument of Hiros…

The paper calculates knot invariants using Blanchfield forms and obstructs sliceness.

The paper studies twisted Alexander polynomials for knot groups in various extensions.

Paper studies convergence of Yang-Mills-Higgs flow on Kähler manifolds.

Solves generalized twisted rabbit problems for higher degree polynomials.

It follows from earlier work of Silver-Williams and the authors that twisted Alexander polynomials detect the unknot and the Hopf link. We now show that twisted Alexander polynomials also detect the trefoil and the figure-8 knot, that twisted Alexander polynomials detect whether a link is split and that twisted Alexand…

Study finds infinite non-fibered twisted torus knots.

Study on realizing subgroup twists in 3-manifolds.

The paper studies knots formed by twisting a circle around a base knot and conjectures a linear growth in crossing numbers.

Twisted torus knots and links are given by twisting adjacent strands of a torus link. They are geometrically simple and contain many examples of the smallest volume hyperbolic knots. Many are also Lorenz links. We study the geometry of twisted torus links and related generalizations. We determine upper bounds on their …

Single twist can unknot certain knots, study shows.

Calculates Dehn twist actions on conformal blocks for modular categories.

Study finds the order of Dehn twists in various groups.