A polynomial time knot polynomial

@article{BarNatan2018APT,
  title={A polynomial time knot polynomial},
  author={Dror Bar-Natan and Roland van der Veen},
  journal={Proceedings of the American Mathematical Society},
  year={2018}
}
  • D. Bar-NatanR. Veen
  • Published 16 August 2017
  • Mathematics, Computer Science
  • Proceedings of the American Mathematical Society
We present the strongest known knot invariant that can be computed effectively (in polynomial time). 

Figures from this paper

A Perturbed-Alexander Invariant

. In this note we give concise formulas, which lead to a simple and fast computer program that computes a powerful knot invariant. This invariant ρ 1 is not new, yet our formulas are by far the

A New Perspective on a Polynomial Time Knot Polynomial

In this work we consider the Z1(K) polynomial time knot polynomial defined and described by Dror Bar-Natan and Roland van der Veen in their 2018 paper ”A polynomial time knot polynomial”. We first

Big Data Approaches to Knot Theory: Understanding the Structure of the Jones Polynomial

A method for using filtrations to analyze infinite data sets where representative sampling is impossible or impractical, an essential requirement for working with knots and the data from knot invariants is introduced.

Framed Knotoids and Their Quantum Invariants

We modify the definition of spherical knotoids to include a framing, in analogy to framed knots, and define a further modification that includes a secondary ‘coframing’ to obtain ‘biframed’ knotoids.

Knot probabilities in equilateral random polygons

We consider the probability of knotting in equilateral random polygons in Euclidean three-dimensional space, which model, for instance, random polymers. Results from an extensive Monte Carlo dataset

Polynomial Invariant of Molecular Circuit Topology

This work presents polynomial invariants that are both efficient and sufficiently powerful to deal with any combination of soft and hard contacts and presents an implementation and table of chains with up to three contacts.

An Unexpected Cyclic Symmetry of $I\mathfrak{u}_n$.

We find and discuss an unexpected (to us) order $n$ cyclic group of automorphisms of the Lie algebra $I\mathfrak{u}_n := \mathfrak{u}_n\ltimes\mathfrak{u}_n^\ast$, where $\mathfrak{u}_n$ is the Lie

AN UNEXPECTED CYCLIC SYMMETRY OF Iun

We find and discuss an unexpected (to us) order n cyclic group of automorphisms of the Lie algebra Iun :“ un ̇ un, where un is the Lie algebra of upper triangular nˆn matrices. Our results also

References

SHOWING 1-10 OF 17 REFERENCES

Quantum Invariants of Knots and 3-Manifolds

This monograph, now in its second revised edition, provides a systematic treatment of topological quantum field theories in three dimensions, inspired by the discovery of the Jones polynomial of

On the 2-loop polynomial of knots

The 2‐loop polynomial of a knot is a polynomial characterizing the 2‐loop part of the Kontsevich invariant of the knot. An aim of this paper is to give a methodology to calculate the 2‐loop

FAST KHOVANOV HOMOLOGY COMPUTATIONS

We introduce a local algorithm for Khovanov homology computations — that is, we explain how it is possible to "cancel" terms in the Khovanov complex associated with a ("local") tangle, hence

Rotational Virtual Knots and Quantum Link Invariants

This paper studies rotational virtual knot theory and its relationship with quantum link invariants. Every quantum link invariant for classical knots and links extends to an invariant of rotational

Quantum Invariants

Abstract:In earlier work, we derived an expression for a partition function ?(λ), and gave a set of analytic hypotheses under which ?(λ) does not depend on a parameter λ. The proof that ?(λ) is

Knots

As indicated by the table of contents, Sections 2 and 3 constitute a start on the subject of knots. Later sections introduce more technical topics. The theme of a relationship of knots with physics

Perturbative Expansion of the Colored Jones Polynomial

ANDREA OVERBAY: Perturbative Expansion of the Colored Jones Polynomial (Under the direction of Lev Rozansky) Both the Alexander polynomial ∆K(t) and the colored Jones polynomial Vα(K; q) are

Wick Ordering for q-Heisenberg algebra

The UniversalR-Matrix, Burau Representation, and the Melvin–Morton Expansion of the Colored Jones Polynomial

Abstract P. Melvin and H. Morton [9] studied the expansion of the colored Jones polynomial of a knot in powers of q −1 and color. They conjectured an upper bound on the power of color versus the

Minimal generating sets of Reidemeister moves

It is well known that any two diagrams representing the same oriented link are related by a finite sequence of Reidemeister moves O1, O2 and O3. Depending on orientations of fragments involved in the