This text is an introduction to classical knot theory. Topics covered include: different constructions of knots; knot diagrams; knot groups; fibred knots; characterization of torus knots; prime decomposition of knots; cyclic coverings; branched coverings and knots; Montesinos links; representations of knot groups; and surgery of 3-manifolds and knots. This edition has been revised and extended to include two new constructions of knot invariants: the Jones and homfly polynomials and the Vassiliev invariants. Most of the topics considered in the book are developed in detail; only the main properties of fundamental groups and some basic results of combinatorial group theory are assumed to be known. The text should be accessible to advanced undergraduate and graduate students in mathematics.
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First Sentence:
The chapter contains an elementary foundation of knot theory. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
metabelian representations, unknotting tunnels, knot manifolds, knot modules, fibred knots, tangle decompositions, unknotting operations, unknotting number one, quantum supergroups, braid automorphism, arborescent links, bracket skein module, periodic knots, satellite knots, cyclic branched coverings, branched covering spaces, pretzel links, singular braids, link concordance, unknotted solid torus, closed incompressible surfaces, hyperbolic knots, skein polynomial, ideal knots, cyclic surgery Key Phrases - Capitalized Phrases (CAPs): (learn more)
Dehn's Lemma, Let Jai New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The chapter contains an elementary foundation of knot theory. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
metabelian representations, unknotting tunnels, knot manifolds, knot modules, fibred knots, tangle decompositions, unknotting operations, unknotting number one, quantum supergroups, braid automorphism, arborescent links, bracket skein module, periodic knots, satellite knots, cyclic branched coverings, branched covering spaces, pretzel links, singular braids, link concordance, unknotted solid torus, closed incompressible surfaces, hyperbolic knots, skein polynomial, ideal knots, cyclic surgery Key Phrases - Capitalized Phrases (CAPs): (learn more)
Dehn's Lemma, Let Jai New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 30
books:
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- Quantum Topology (Series on Knots and Everything) by Louis H. Kauffman on 4 pages
- Knot Groups. Annals of Mathematics Studies. (Annals of Mathematics Studies, No. 56) by Lee Paul Neuwirth in Front Matter, and Back Matter
- Measure and Integration Theory (Sammlung Guttentag) by Heinz Bauer in Front Matter
- Probability Theory (De Gruyter Studies in Mathematics) by Heinz Bauer in Front Matter
- Surfaces and planar discontinuous groups (Lecture notes in mathematics) by Heiner Zieschang in Back Matter
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