4 edition of High Dimensional Knotting found in the catalog.
|Statement||World Scientific Publishing Co Pte Ltd|
|Publishers||World Scientific Publishing Co Pte Ltd|
|The Physical Object|
|Pagination||xvi, 116 p. :|
|Number of Pages||41|
nodata File Size: 7MB.
The book is a bit informal and, in these notes, some claims are not proved High Dimensional Knotting instead justified with statements like "Livingston claims. Combinatorial tools often appear as unnatural or ad hoc.
Raymond Lickorish's An Introduction Knot Theory, Graduate Texts in Mathematics 175, NY: Springer-Verlag, 1997. What is perhaps most surprising is that many problems that are intractable in the classical case have been solved for high-dimensional knots. " Such claims are sometimes justified by referencing sources which provide detailed proofs.
A Century of Knot Theory. The genus is an important example. Although his approach was algebraic, the Jones polynomial was soon reinterpreted combinatorially. Printouts of Proofs from Section 5.
These notes and supplements have not been classroom tested and so may have some typographical errors. The goal for now is to demonstrate how the notion of knotting can be given a rigorous mathematical formulation, and to give the reader a flavor of the problems and. Fortunately, its properties can be revealed by mapping it onto simpler, finite, groups.
There is also a strong interplay between knot theory in different High Dimensional Knotting, and this interplay leads to an array of new topics at the border of the classical and high-dimensional settings.
Note that the boundary, or edge, of the surface is a knotted curve. Periodic Seifert Surfaces and Edmonds' Theorem.
The techniques of knot theory which are based on the study of knot diagrams are called combinatorial methods. The Definition of a Knot. Have an idea for a project that will add value for arXiv's community? Printouts of Proofs from Section 4.
Copies of the classnotes are on the internet in PDF format as given below.
Visualization is an important part of this journey and techniques for higher dimensions, especially in 4-dimensional space, are discussed in detail.