Knot theory is a rapidly developing field of research with many applications not only for
mathematics. The present volume, written by a well-known specialist, gives a complete …

" Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics.
This enyclopedia is filled with valuable information on a rich and fascinating subject."–Ed …

We give examples of knots with some unusual properties of the crossing number of positive
diagrams or strand number of positive braid representations. In particular, we show that …

We classify all knot diagrams of genus two and three, and give applications to positive,
alternating and homogeneous knots, including a classification of achiral genus 2 alternating …

We show that nontrivial classical pretzel knots L (p, q, r) are hyperbolic with eight exceptions
which are torus knots. We find Conway polynomials of n-pretzel links using a new …

Using the band representation of the 3-strand braid group, it is shown that the genus of 3-
braid links can be read off their skein polynomial. Some applications are given, in particular …

DNA cages are kind of artificial polyhedra that are interlinked and interlocked with DNA
double-strands. A simple formula to calculate genus of DNA cages is presented here. The …

In this paper, we will strengthen the known upper and lower bounds on the delta-crossing
number of knots in terms of the triple-crossing number. The latter bound turns out to be …

Free genus one knots with large volume Page 1 Pacific Journal of Mathematics FREE
GENUS ONE KNOTS WITH LARGE VOLUME Mark Brittenham Volume 201 No. 1 …

The model of polyhedral links has been applied to explain DNA and protein cages from
mathematics. Recently, a type of polyhedral links has been constructed by the means of …