Knot theory & its applications
著者
書誌事項
Knot theory & its applications
（Modern Birkhäuser classics）
Birkhäuser, c2008
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Musubime riron to sono ōyō
Knot theory and its applications
結び目理論とその応用
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注記
"Reprint of the 1996 edition."
Includes bibliographical references (p. [333]-336) and index
"Originally published as a monograph"
1996 ed.: [by] Kunio Murasugi ; translated by Bohdan Kurpita
内容説明・目次
内容説明
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.
目次
Fundamental Concepts of Knot Theory.- Knot Tables.- Fundamental Problems of Knot Theory.- Classical Knot Invariants.- Seifert Matrices.- Invariants from the Seifert Matrix.- Torus Knots.- Creating Manifolds from Knots.- Tangles and 2-Bridge Knots.- The Theory of Braids.- The Jones Revolution.- Knots via Statistical Mechanics.- Knot Theory in Molecular Biology.- Graph Theory Applied to Chemistry.- Vassiliev Invariants.
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