Related papers: Some notes on the inverse problem for braids

We use Ozsv\'ath, Stipsicz, and Szab\'o's Upsilon-invariant to provide bounds on cobordisms between knots that `contain full-twists'. In particular, we recover and generalize a classical consequence of the Morton-Franks-Williams inequality…

We find further evidence for the conjecture relating large N Chern-Simons theory on S^3 with topological string on the resolved conifold geometry by showing that the Wilson loop observable of a simple knot on S^3 (for any representation)…

This is part of a series of papers on the inverse spectral problem for bounded analytic plane domains. Here, we use the trace formula established in the first paper (`Balian-Bloch trace formula') to explicitly calculate wave trace…

We show that embedding calculus invariants $ev_n$ are surjective for long knots in an arbitrary $3$-manifold. This solves some remaining open cases of Goodwillie--Klein--Weiss connectivity estimates, and at the same time confirms one half…

In this paper we discuss the applications of knotoids to modelling knots in open curves and produce new knotoid invariants. We show how invariants of knotoids generally give rise to well-behaved measures of how much an open curve is…

We discuss different invariants of knots and links that depend on a primitive root of unity. We clarify the definitions of existing invariants with the Reshetikhin-Turaev method, present the generalization of ADO invariants to…

We categorify the notion of an infinitesimal braiding in a linear strict symmetric monoidal category, leading to the notion of a (strict) infinitesimal 2-braiding in a linear symmetric strict monoidal 2-category. We describe the associated…

The alternating knots, links and twists projected on the $S_2$ sphere were identified with the phase space of a Hamiltonian dynamic system of one degree of freedom. The saddles of the system correspond to the crossings, the edges correspond…

We introduce an invariant of tangles in Khovanov homology by considering a natural inverse system of Khovanov homology groups. As application, we derive an invariant of strongly invertible knots; this invariant takes the form of a graded…

We construct a topological invariant of algebraic plane curves, which is in some sense an adaptation of the linking number of knot theory. This invariant is shown to be a generalization of the I-invariant of line arrangements developed by…

In this paper we introduce a new invariant of virtual knots and links that is non-trivial for infinitely many virtuals, but is trivial on classical knots and links. The invariant is initially be expressed in terms of a relative of the…

We point out the connection between mathematical knot theory and spin glass/search problem. In particular, we present a statistical mechanical formulation of the problem of computing a knot invariant; p-colorability problem, which provides…

We discuss how to apply work of L. Rudolph to braid conjugacy class invariants to obtain potentially effective obstructions to a slice knot being ribbon. We then apply these ideas to a family of braid conjugacy class invariants coming from…

Burau representation of the Artin braid group remains as one of the very important representations for the braid group. Partly, because of its connections to the Alexander polynomial which is one of the first and most useful invariants for…

This paper continues the study of finite-type invariants of homology spheres studied by Ohtsuki and Garoufalidis. We apply the surgery classification of links to give a diagrammatic description, using ideas of Ohtsuki. This uses a…

Braid theory is used to calcualte the topological entropy of data from the belousov-Zhabotinskii reaction, the results agree well with one-dimensional theory to the order of approximation considered.

Let M be a closed oriented 3-manifold with first Betti number one. Its equivariant linking pairing may be seen as a two-dimensional cohomology class in an appropriate infinite cyclic covering of the configuration space of ordered pairs of…

Construction of representations of braid group generators from $N$-state vertex models provide an elegant route to study knot and link invariants. Using such a braid group representation, an algebraic formula for the link invariants was put…

It has been folklore for several years in the knot theory community that certain integrals on configuration space, originally motivated by perturbation theory for the Chern-Simons field theory, converge and yield knot invariants. This was…

We construct an algebra of non-trivial homological operations on Khovanov homology with coefficients in $\mathbb Z_2$ generated by two Bockstein operations. We use the unified Khovanov homology theory developed by the first author to lift…