Knot Theory and Its Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Knot Theory and Its Applications write by Kunio Murasugi. This book was released on 2009-12-29. Knot Theory and Its Applications available in PDF, EPUB and Kindle. This 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.
Introductory Lectures on Knot Theory
Introductory Lectures on Knot Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introductory Lectures on Knot Theory write by Louis H. Kauffman. This book was released on 2012. Introductory Lectures on Knot Theory available in PDF, EPUB and Kindle. More recently, Khovanov introduced link homology as a generalization of the Jones polynomial to homology of chain complexes and Ozsvath and Szabo developed Heegaard-Floer homology, that lifts the Alexander polynomial. These two significantly different theories are closely related and the dependencies are the object of intensive study. These ideas mark the beginning of a new era in knot theory that includes relationships with four-dimensional problems and the creation of new forms of algebraic topology relevant to knot theory. The theory of skein modules is an older development also having its roots in Jones discovery. Another significant and related development is the theory of virtual knots originated independently by Kauffman and by Goussarov Polyak and Viro in the '90s. All these topics and their relationships are the subject of the survey papers in this book.
The Mathematics of Knots
The Mathematics of Knots - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Mathematics of Knots write by Markus Banagl. This book was released on 2010-11-25. The Mathematics of Knots available in PDF, EPUB and Kindle. The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented; numerous illustrations support the text. The book will be of great interest to researchers in topology, geometry, and mathematical physics, graduate students specializing in knot theory, and cell biologists interested in the topology of DNA strands.
The Knot Book
The Knot Book - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Knot Book write by Colin Conrad Adams. This book was released on 2004. The Knot Book available in PDF, EPUB and Kindle. Knots 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.
Physical and Numerical Models in Knot Theory
Physical and Numerical Models in Knot Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Physical and Numerical Models in Knot Theory write by Jorge Alberto Calvo. This book was released on 2005. Physical and Numerical Models in Knot Theory available in PDF, EPUB and Kindle. The 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.
