High-dimensional knotting : an illustrated guide / Dennis Roseman, University of Iowa, USA.

Format:

Book

Author/Creator:

Roseman, Dennis, 1939- Author.

Series:

K & E series on knots and everything ; 0219-9769 v. 79.

Series on knots and everything, 0219-9769 ; vol. 79

Language:

English

Subjects (All):

Knot theory.

Four-manifolds (Topology).

Physical Description:

xiv, 500 pages : illustrations ; 24 cm.

illustrations.

Place of Publication:

Singapore ; Hackensack, NJ : World Scientific, [2026]

Summary:

"Focused on concrete examples and constructions and using extensive computer generated three-dimensional graphics, this book serves as a guide to methods and examples of higher dimensional knotting. The book has modest mathematical requirements, has been written with non-specialists in mind and contains considerable background information. Knotting whether fanciful or practical has been of interest to many - from sculptors to sailors and in more modern times of interest to mathematicians, biologists and physicists as well. Spaces of dimensions greater than three are also of widespread interest in the arts, sciences and engineering as well as mathematics. Knotting and linking of circles can aid us to understand three dimensionality. So, it is natural to consider knotting in order to understand higher dimensions. Knotting in 4-dimensional space involves surfaces - spheres, tori, Klein bottles and others while in five dimensions one looks primarily at similar tangling and self-tangling of three dimensional objects. Visualization is an important part of this journey and techniques for higher dimensions, especially in 4-dimensional space, are discussed in detail"-- Provided by publisher.

Contents:

Basics

Elements of geometric topology

Overview of knottings

Topology topics of 1-knottings

Knotting, dimension and codimension

Projections of 2-knottings

Knot-moves

Slicing surfaces in 4-space

Ribbon constructions for surface knottings

Spinning constructions for surface knottings

Some final topics for 2-knottings

Higher-dimensional knotting basics.

Notes:

Includes bibliographical references and index.

ISBN:

9789813237391

9813237392

OCLC:

1551431098