On Types of Knotted Curves
Author: Garland B. Briggs
Publisher:
Published: 1927
Total Pages: 38
ISBN-13:
DOWNLOAD EBOOKPosts
The Knot Book
Author: Colin Conrad Adams
Publisher: American Mathematical Soc.
Published: 2004
Total Pages: 330
ISBN-13: 0821836781
DOWNLOAD EBOOKKnots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.
Mathematics
Author: Keith J. Devlin
Publisher: Columbia University Press
Published: 1999
Total Pages: 340
ISBN-13: 9780231116398
DOWNLOAD EBOOKA modern classic by an accomplished mathematician and best-selling author has been updated to encompass and explain the recent headline-making advances in the field in non-technical terms.
Canadian Journal of Mathematics
Author:
Publisher:
Published: 1950
Total Pages: 128
ISBN-13:
DOWNLOAD EBOOKKnots and Links
Author: Dale Rolfsen
Publisher: American Mathematical Soc.
Published: 2003
Total Pages: 458
ISBN-13: 0821834363
DOWNLOAD EBOOKRolfsen's beautiful book on knots and links can be read by anyone, from beginner to expert, who wants to learn about knot theory. Beginners find an inviting introduction to the elements of topology, emphasizing the tools needed for understanding knots, the fundamental group and van Kampen's theorem, for example, which are then applied to concrete problems, such as computing knot groups. For experts, Rolfsen explains advanced topics, such as the connections between knot theory and surgery and how they are useful to understanding three-manifolds. Besides providing a guide to understanding knot theory, the book offers 'practical' training. After reading it, you will be able to do many things: compute presentations of knot groups, Alexander polynomials, and other invariants; perform surgery on three-manifolds; and visualize knots and their complements.It is characterized by its hands-on approach and emphasis on a visual, geometric understanding. Rolfsen offers invaluable insight and strikes a perfect balance between giving technical details and offering informal explanations. The illustrations are superb, and a wealth of examples are included. Now back in print by the AMS, the book is still a standard reference in knot theory. It is written in a remarkable style that makes it useful for both beginners and researchers. Particularly noteworthy is the table of knots and links at the end. This volume is an excellent introduction to the topic and is suitable as a textbook for a course in knot theory or 3-manifolds. Other key books of interest on this topic available from the AMS are ""The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace your Shoes"" and ""The Knot Book.""
Knot Theory and Its Applications
Author: Kunio Murasugi
Publisher: Springer Science & Business Media
Published: 2009-12-29
Total Pages: 348
ISBN-13: 0817647198
DOWNLOAD EBOOKThis book introduces the study of knots, providing insights into recent applications in DNA research and graph theory. It sets forth fundamental facts such as knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials. It also covers more recent developments and special topics, such as chord diagrams and covering spaces. The author avoids advanced mathematical terminology and intricate techniques in algebraic topology and group theory. Numerous diagrams and exercises help readers understand and apply the theory. Each chapter includes a supplement with interesting historical and mathematical comments.
Reading Images and Seeing Words
Author:
Publisher: BRILL
Published: 2021-11-01
Total Pages: 200
ISBN-13: 9004486704
DOWNLOAD EBOOKThe simultaneously tautological and oxymoronic nature of word / image relations has become a subject of massive debate in the post-modern period. This is not only because of the increasing predominance of word / image messages within our modern media-saturated culture, but also because intellectual disciplines are becoming increasingly sensitized to the essentially hybrid nature of the way we construct meaning in the world. The essays in this volume offer an exemplary insight into both aspects of this phenomenon. Focussing on both traditional and modern media (theatre, fiction, poetry, graphic art, cinema), the essays of Reading Images and Seeing Words are deeply concerned to show how it is according to signifying codes (rhetoric, poetics, metaphor), that meaning and knowledge are produced. Not the least value of this collection is the insight it gives into the multiple models of word / image interaction and the rich ambiguity of the tautological and oxymoronic relations they embody.
Physical and Numerical Models in Knot Theory
Author: Jorge Alberto Calvo
Publisher: World Scientific
Published: 2005
Total Pages: 642
ISBN-13: 9812703462
DOWNLOAD EBOOKThe physical properties of knotted and linked configurations in space have long been of interest to mathematicians. More recently, these properties have become significant to biologists, physicists, and engineers among others. Their depth of importance and breadth of application are now widely appreciated and valuable progress continues to be made each year. This volume presents several contributions from researchers using computers to study problems that would otherwise be intractable. While computations have long been used to analyze problems, formulate conjectures, and search for special structures in knot theory, increased computational power has made them a staple in many facets of the field. The volume also includes contributions concentrating on models researchers use to understand knotting, linking, and entanglement in physical and biological systems. Topics include properties of knot invariants, knot tabulation, studies of hyperbolic structures, knot energies, the exploration of spaces of knots, knotted umbilical cords, studies of knots in DNA and proteins, and the structure of tight knots. Together, the chapters explore four major themes: physical knot theory, knot theory in the life sciences, computational knot theory, and geometric knot theory.
Grid Homology for Knots and Links
Author: Peter S. Ozsváth
Publisher: American Mathematical Soc.
Published: 2015-12-04
Total Pages: 423
ISBN-13: 1470417375
DOWNLOAD EBOOKKnot theory is a classical area of low-dimensional topology, directly connected with the theory of three-manifolds and smooth four-manifold topology. In recent years, the subject has undergone transformative changes thanks to its connections with a number of other mathematical disciplines, including gauge theory; representation theory and categorification; contact geometry; and the theory of pseudo-holomorphic curves. Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory, specifically as it relates to some of the above developments. After a brief overview of the background material in the subject, the book gives a self-contained treatment of knot Floer homology from the point of view of grid diagrams. Applications include computations of the unknotting number and slice genus of torus knots (asked first in the 1960s and settled in the 1990s), and tools to study variants of knot theory in the presence of a contact structure. Additional topics are presented to prepare readers for further study in holomorphic methods in low-dimensional topology, especially Heegaard Floer homology. The book could serve as a textbook for an advanced undergraduate or part of a graduate course in knot theory. Standard background material is sketched in the text and the appendices.
A Survey of Knot Theory
Author: Akio Kawauchi
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 431
ISBN-13: 3034892276
DOWNLOAD EBOOKKnot 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 survey of this theory from its very beginnings to today's most recent research results. An indispensable book for everyone concerned with knot theory.
