Knot Theory and Its Applications

Knot theory is a concept in algebraic topology that has found applications to a variety of mathematical problems as well as in computer science, biological and medical research, and mathematical physics. This book is directed to a broad audience of research workers and beginning graduate students in these fields. It contains most of the fundamental classical facts about the theory, such as knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials, as well as more recent developments and special topics such as chord diagrams and covering spaces. With over 300 illustrations, the book balances theory with visualization. It is an introduction to the fascinating study of knots and provides insight into recent applications to such studies as DNA research and graph theory.