## On Knots
Then come branched covering spaces, the Alexander polynomial, signature theorems, the work of Casson and Gordon on slice knots, and a chapter on knots and algebraic singularities.The book concludes with an appendix about generalized polynomials. |

### What people are saying - Write a review

This is an excellent and clear book to understand knot theory. It is easy to read and easy to understand. It is great for self study and also for research in knot theory.

### Contents

INTRODUCTION | 3 |

LINKING NUMBERS AND REIDEMEISTER MOVES | 9 |

THE CONWAY POLYNOMIAL | 19 |

EXAMPLES AND SKEIN THEORY | 42 |

DETECTING SLICES AND RIBBONS A FIRST PASS | 70 |

MISCELLANY | 93 |

Rope Trick | 98 |

Topological Script | 100 |

The Mobius Band | 152 |

The Generalized Polynomial | 155 |

The Generalized Polynomial and Regular Isotopy | 163 |

Twisted Bands | 179 |

SPANNING SURFACES AND SEIFERT PAIRING | 181 |

RIBBONS AND SLICES | 208 |

ALEXANDER POLYNOMIAL AND BRANCHED COVERINGS | 229 |

ALEXANDER POLYNOMIAL AND ARF INVARIANT | 252 |

Calculi | 103 |

Infinite Forms | 106 |

Quandles | 110 |

Topology of DNA | 113 |

Knots Are Decorated Fibonacci Trees | 115 |

Alhambra Mosaic | 120 |

Odd Knot | 121 |

Pilars Family Tree | 122 |

The Untwisted Double of the Double of the Figure Eight Knot | 123 |

Applied ScriptA Ribbon Surface | 124 |

Kirkhoffs Matrix Tree Theorem | 129 |

States and Trails | 132 |

The Map Theorem | 147 |

FREE DIFFERENTIAL CALCULUS | 262 |

CYCLIC BRANCHED COVERINGS | 271 |

SIGNATURE THEOREMS | 299 |

GSIGNATURE THEOREM FOR FOURMANIFOLDS | 327 |

SIGNATURE OF CYCLIC BRANCHED COVERINGS | 332 |

AN INVARIANT FOR COVERINGS | 337 |

SLICE KNOTS | 345 |

CALCULATING a FOR GENERALIZED STEVEDORES KNOTS T | 355 |

SINGULARITIES KNOTS AND BRIESKORN VARIETIES | 366 |

Generalized Polynomials and a States Model for the Jones Polynomial | 417 |

Knot Tables and the LPolynomial | 444 |

REFERENCES | 474 |