Related papers: Lorenz knots

This is a short expository article on alternating knots and is to appear in the Concise Encyclopedia of Knot Theory.

This article is a survey on Lorenz knots. We describe the original construction, prove several classical properties, in particular the fact that the closure of a positive braid is a fibered knot, and describe Ghys'correspondance between…

The aim of this survey article is to highlight several notoriously intractable problems about knots and links, as well as to provide a brief discussion of what is known about them.

This is a survey paper on Legendrian and transversal knots for Handbook of Knot Theory.

In this essay dedicated to Yakov Eliashberg we survey the current state of the field of Lagrangian (un)knots, reviewing some constructions and obstructions along with a number of unsolved questions. The appendix by Georgios Dimitroglou…

We construct a new type of geometric knot theory, plumbers' knots, and solve the problems of distinguishing and enumerating such knots at a fixed level of complexity. (v2) Minor edits, added theorem 3.18. (v3) Substantial revisions,…

This paper is a review of the book "Knots" by Alexei Sossinsky. The review includes a short personal history of knot theory at the end of the twentieth century.

This paper visualizes a knot reduction algorithm

The aim of this paper is to realise the techniques of picture-valued invariants and invariants valued in free groups for long knots in the full torus. Such knots and links are of a particular interest because of their relation to Legendrian…

We exhibit low-dilatation families of surface homeomorphisms among monodromies of Lorenz knots.

Although most knots are nonalternating, modern research in knot theory seems to focus on alternating knots. We consider here nonalternating knots and their properties. Specifically, we show certain classes of knots have nontrivial Jones…

Twisted torus knots are torus knots with some full twists added along some number of adjacent strands. There are infinitely many known examples of twisted torus knots which are actually torus knots. We give eight more infinite families of…

This is an expository article on diagrammatic representations of knots and links in various settings via braids.

We review recent developments in the theory of Thompson group representations related to knot theory.

We introduce a relation of cobordism for knots in thickened surfaces and study cobordism invariants of such knots.

This article is solicited by C.\ Adams for a special issue of {\it Chaos, Solitons and Fractals\/} devoted to knot theory and its applications. We present some recent results about Dehn surgeries on arborescent knots and links.

We construct infinitely many families of Lorenz knots that are satellites but not cables, giving counterexamples to a conjecture attributed to Morton. We amend the conjecture to state that Lorenz knots that are satellite have companion a…

This article gives a foundational account of various characterizations of framed links in the $3$-sphere.

The unknotting number of a positive braid with n strands and k intersections is known to be equal to (k-n+1)/2. We consider Lorenz knots (which are positive braids) and, using a different method, find their unknotting numbers in terms of…

The contents of this 6-page paper have been subsumed into the 13-page paper, "A note on closed 3-braids", arXiv:0802.1072 [math.GT]. This paper is correct, but contains less information than the new one. The topological classification of…