1.

Record Nr.

UNINA9910154751303321

Autore

Kauffman Louis H.

Titolo

On Knots. (AM-115), Volume 115 / / Louis H. Kauffman

Pubbl/distr/stampa

Princeton, NJ : , : Princeton University Press, , [2016]

©2016

ISBN

1-4008-8213-3

Descrizione fisica

1 online resource (497 pages) : illustrations

Collana

Annals of Mathematics Studies ; ; 121

Disciplina

514/.224

Soggetti

Knot theory

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di bibliografia

Bibliography.

Nota di contenuto

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

Sommario/riassunto

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.

2.

Record Nr.

UNISA996466118903316

Titolo

Advanced Functional Programming : First International Spring School on Advanced Functional Programming Techniques, Bastad, Sweden, May 24 - 30, 1995. Tutorial Text / / edited by Johan Jeuring, Erik Meijer

Pubbl/distr/stampa

Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1995

ISBN

3-540-49270-4

Edizione

[1st ed. 1995.]

Descrizione fisica

1 online resource (VII, 336 p.)

Collana

Lecture Notes in Computer Science, , 0302-9743 ; ; 925

Soggetti

Functional programming (Computer science)

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di contenuto

Functional parsers -- Monads for functional programming -- The design of a pretty-printing library -- Functional programming with overloading and higher-order polymorphism -- Programming with Fudgets -- Constructing medium sized efficient functional programs in Clean -- Merging monads and folds for functional programming -- Programming with algebras -- Graph algorithms with a functional flavour.

Sommario/riassunto

This volume presents the tutorials given during the First International Spring School on Advanced Functional Programming Techniques, held in Bastad, Sweden in May 1995. The last few years have seen important new developments in functional programming techniques: concepts, such as monads, type classes, and several new special purpose libraries of higher-order functions are new and powerful methods for



structuring programs. This book brings programmers, software engineers and computer scientists up-to-date with the latest techniques. Most tutorial contributions contain exercises to familiarize the reader with the new concepts and techniques, and only basic knowledge in functional programming is assumed.