E-Book, Englisch, 498 Seiten
Kauffman On Knots
1. Auflage 2016
ISBN: 978-1-4008-8213-7
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
E-Book, Englisch, 498 Seiten
Reihe: Annals of Mathematics Studies
ISBN: 978-1-4008-8213-7
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
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 paves the way for later discussion of the recently discovered Jones and generalized polynomials. The central chapter, Chapter Six, is a miscellany of topics and recreations. Here the reader will find the quaternions and the belt trick, a devilish rope trick, Alhambra mosaics, Fibonacci trees, the topology of DNA, and the author's geometric interpretation of the generalized Jones Polynomial.
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.
Autoren/Hrsg.
Weitere Infos & Material
Frontmatter, pg. i
CONTENTS, pg. vii
PREFACE, pg. ix
I. INTRODUCTION, pg. 1
II. LINKING NUMBERS AND REIDEMEISTER MOVES, pg. 9
III. THE CONWAY POLYNOMIAL, pg. 19
IV. EXAMPLE S AND SKEIN THEORY, pg. 42
V. DETECTING SLICES AND RIBBONS— A FIRST PASS, pg. 70
VI. MISCELLANY, pg. 92
VII. SPANNING SURFACES AND THE SEIFERT PAIRING, pg. 181
VIII. RIBBONS AND SLICES, pg. 208
IX. THE ALEXANDER POLYNOMIAL AND BRANCHED COVERINGS, pg. 229
X. THE ALEXANDER POLYNOMIAL AND THE ARF INVARIANT, pg. 252
XI. FREE DIFFERENTIAL CALCULUS, pg. 262
XII. CYCLIC BRANCHED COVERINGS, pg. 271
XIII. SIGNATURE THEOREMS, pg. 299
XIV. G-SIGNATURE THEOREM FOR FOUR MANIFOLDS, pg. 327
XV. SIGNATURE OF CYCLIC BRANCHED COVERINGS, pg. 332
XVI. AN INVARIANT FOR COVERINGS, pg. 337
XVII. SLICE KNOTS, pg. 345
XVIII. CALCULATING sr FOR GENERALIZED STEVEDORE’S KNOT, pg. 355
XIX. SINGULARITIES, KNOTS AND BRIESKORN VARIETIES, pg. 366
APPENDIX. GENERALIZED POLYNOMIALS AND A STATE MODEL FOR THE JONES POLYNOMIAL, pg. 417
KNOT TABLES AND THE L-POLYNOMIAL, pg. 444
REFERENCES, pg. 474
