On Knots. (AM-115), Volume 115 / / Louis H. Kauffman.
On Knots is a journey through the theory of knots, starting from the simplest combinatorial ideas--ideas arising from the representation of weaving patterns. From this beginning, topological invariants are constructed directly: first linking numbers, then the Conway polynomial and skein theory. This...
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| Superior document: | Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 |
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| VerfasserIn: | |
| Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2016] ©1988 |
| Year of Publication: | 2016 |
| Language: | English |
| Series: | Annals of Mathematics Studies ;
115 |
| Online Access: | |
| Physical Description: | 1 online resource (498 p.) |
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Table of Contents:
- Frontmatter
- CONTENTS
- PREFACE
- I. INTRODUCTION
- II. LINKING NUMBERS AND REIDEMEISTER MOVES
- III. THE CONWAY POLYNOMIAL
- IV. EXAMPLE S AND SKEIN THEORY
- V. DETECTING SLICES AND RIBBONS- A FIRST PASS
- VI. MISCELLANY
- VII. SPANNING SURFACES AND THE SEIFERT PAIRING
- VIII. RIBBONS AND SLICES
- IX. THE ALEXANDER POLYNOMIAL AND BRANCHED COVERINGS
- X. THE ALEXANDER POLYNOMIAL AND THE ARF INVARIANT
- XI. FREE DIFFERENTIAL CALCULUS
- XII. CYCLIC BRANCHED COVERINGS
- XIII. SIGNATURE THEOREMS
- XIV. G-SIGNATURE THEOREM FOR FOUR MANIFOLDS
- XV. SIGNATURE OF CYCLIC BRANCHED COVERINGS
- XVI. AN INVARIANT FOR COVERINGS
- XVII. SLICE KNOTS
- XVIII. CALCULATING σr FOR GENERALIZED STEVEDORE'S KNOT
- XIX. SINGULARITIES, KNOTS AND BRIESKORN VARIETIES
- APPENDIX. GENERALIZED POLYNOMIALS AND A STATE MODEL FOR THE JONES POLYNOMIAL
- KNOT TABLES AND THE L-POLYNOMIAL
- REFERENCES