𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A Combinatorial Description of Knotted Surfaces and Their Isotopies

✍ Scribed by J.Scott Carter; Joachim H. Rieger; Masahico Saito

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
747 KB
Volume
127
Category
Article
ISSN
0001-8708

No coin nor oath required. For personal study only.

✦ Synopsis

We discuss the diagrammatic theory of knot isotopies in dimension 4. We project a knotted surface to a three-dimensional space and arrange the surface to have generic singularities upon further projection to a plane. We examine the singularities in this plane as an isotopy is performed, and give a finite set of local moves to the singular set that can be used to connect any two isotopic knottings. We show how the notion of projections of isotopies can be used to give a combinatoric description of knotted surfaces that is sufficient for categorical applications. In this description, knotted surfaces are presented as sequences of words in symbols, and there is a complete list of moves among such sequences that relate the symbolic representations of isotopic knotted surfaces.

πŸ“œ SIMILAR VOLUMES

Modelling supercoiled DNA knots and cate
Modelling supercoiled DNA knots and catenanes by means of a new regular isotopy invariant
✍ S. A. Wilkinson πŸ“‚ Article πŸ“… 1991 πŸ› Springer Netherlands 🌐 English βš– 895 KB

This paper extends the knot polynomial classification of DNA knots and catenanes, by incorporating a measure of supercoiling. Cozzarelli, Millett, and White have used the Jones polynomial and the generalised 2-variable polynomial to describe the products of iterated Tn 3 resoivase recombination and

A combinatorial application of matrix Ri
A combinatorial application of matrix Riccati equations and their q-analogue
✍ G.B. Collins; J.P. Goulden; D.M. Jackson; A.M. Nierstrasz πŸ“‚ Article πŸ“… 1981 πŸ› Elsevier Science 🌐 English βš– 737 KB

The generating functions for a large class of combinatorial problems involving the enumeration of permutations may be expressed as solutions to matrix Riccati equations. We show that the generating functions for the permutation problem in which the number of inversions is also preserved form a syste