## A Survey of Knot TheoryKnot 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 knot theory from its very beginnings to today's most recent research results. The topics include Alexander polynomials, Jones type polynomials, and Vassiliev invariants. The book can serve as an introduction to the field for advanced undergraduate and graduate students. Also researchers working in outside areas such as theoretical physics or molecular biology will benefit from this thorough study which is complemented by many exercises and examples. |

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### Contents

Presentations | 7 |

Standard examples | 21 |

Compositions and decompositions | 31 |

Copyright | |

20 other sections not shown

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### Common terms and phrases

abelian Acad Alexander polynomial algebraic ambient isotopic Amer amphicheiral auto-homeomorphism boundary braid group Bull called Cambridge Philos cobordism compact component connected sum Contemp Conway Corollary cyclic covering decomposition denote dimensional disk embedded equivalent Exercise exterior fibered field theory finite following theorem fundamental group genus Geom geometry graph Heegaard Helv homeomorphism homology 3-spheres homotopy hyperbolic 3-manifolds integer isomorphism isotopy Jones polynomial Kawauchi knot groups knot theory Knot Theory Ramifications knots and links Lecture Notes Lemma link diagram link invariants link polynomials London Math loop module non-trivial Notes in Math obtained oriented 3-manifold pair Phys polynomial invariants prime prime knots Proc Publ quantum representations ribbon 2-knot Seifert circles Seifert manifold Seifert matrix Seifert surface shown in figure skein polynomial slice knot sphere Springer Verlag subgroup sutured manifold tangle Topology Appl torus knot Trans trivial knot Walter de Gruyter World Sci