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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Kauffman, Louis H., author. aut http://id.loc.gov/vocabulary/relators/aut On Knots. (AM-115), Volume 115 / Louis H. Kauffman. Princeton, NJ : Princeton University Press, [2016] ©1988 1 online resource (498 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 115 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 restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Knot theory. MATHEMATICS / Topology. bisacsh 3-sphere. Addition theorem. Addition. Alexander polynomial. Algebraic variety. Algorithm. Ambient isotopy. Arf invariant. Basepoint. Bijection. Bilinear form. Borromean rings. Bracket polynomial. Braid group. Branched covering. Chiral knot. Chromatic polynomial. Cobordism. Codimension. Combination. Combinatorics. Complex analysis. Concentric. Conjecture. Connected sum. Conway polynomial (finite fields). Counting. Covering space. Cyclic group. Dense set. Determinant. Diagram (category theory). Diffeomorphism. Dimension. Disjoint union. Disk (mathematics). Dual graph. Elementary algebra. Embedding. Enumeration. Existential quantification. Exotic sphere. Fibration. Formal power series. Fundamental group. Geometric topology. Geometry and topology. Geometry. Group action. Homotopy. Integer. Intersection form (4-manifold). Isolated singularity. Jones polynomial. Knot complement. Knot group. Laws of Form. Lens space. Linking number. Manifold. Module (mathematics). Morwen Thistlethwaite. Normal bundle. Notation. Obstruction theory. Operator algebra. Pairing. Parity (mathematics). Partition function (mathematics). Planar graph. Point at infinity. Polynomial ring. Polynomial. Quantity. Rectangle. Reidemeister move. Remainder. Root of unity. Saddle point. Seifert surface. Singularity theory. Slice knot. Special case. Statistical mechanics. Substructure. Summation. Symmetry. Theorem. Three-dimensional space (mathematics). Topological space. Torus knot. Trefoil knot. Tubular neighborhood. Underpinning. Unknot. Variable (mathematics). Whitehead link. Wild knot. Writhe. Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496 print 9780691084350 https://doi.org/10.1515/9781400882137 https://www.degruyter.com/isbn/9781400882137 Cover https://www.degruyter.com/document/cover/isbn/9781400882137/original |
language |
English |
format |
eBook |
author |
Kauffman, Louis H., Kauffman, Louis H., |
spellingShingle |
Kauffman, Louis H., Kauffman, Louis H., On Knots. (AM-115), Volume 115 / Annals of Mathematics Studies ; 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 |
author_facet |
Kauffman, Louis H., Kauffman, Louis H., |
author_variant |
l h k lh lhk l h k lh lhk |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Kauffman, Louis H., |
title |
On Knots. (AM-115), Volume 115 / |
title_full |
On Knots. (AM-115), Volume 115 / Louis H. Kauffman. |
title_fullStr |
On Knots. (AM-115), Volume 115 / Louis H. Kauffman. |
title_full_unstemmed |
On Knots. (AM-115), Volume 115 / Louis H. Kauffman. |
title_auth |
On Knots. (AM-115), Volume 115 / |
title_alt |
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 |
title_new |
On Knots. (AM-115), Volume 115 / |
title_sort |
on knots. (am-115), volume 115 / |
series |
Annals of Mathematics Studies ; |
series2 |
Annals of Mathematics Studies ; |
publisher |
Princeton University Press, |
publishDate |
2016 |
physical |
1 online resource (498 p.) Issued also in print. |
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 |
isbn |
9781400882137 9783110494914 9783110442496 9780691084350 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA612 |
callnumber-sort |
QA 3612.2 K3 |
url |
https://doi.org/10.1515/9781400882137 https://www.degruyter.com/isbn/9781400882137 https://www.degruyter.com/document/cover/isbn/9781400882137/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
514 - Topology |
dewey-full |
514.2 |
dewey-sort |
3514.2 |
dewey-raw |
514.2 |
dewey-search |
514.2 |
doi_str_mv |
10.1515/9781400882137 |
oclc_num |
979728851 |
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Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 |
is_hierarchy_title |
On Knots. (AM-115), Volume 115 / |
container_title |
Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 |
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"><subfield code="a">Partition function (mathematics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Planar graph.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Point at infinity.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Polynomial ring.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Polynomial.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Quantity.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Rectangle.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Reidemeister move.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Remainder.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Root of unity.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Saddle point.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Seifert surface.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Singularity theory.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Slice knot.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Special case.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Statistical mechanics.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Substructure.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Summation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Symmetry.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Theorem.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Three-dimensional space (mathematics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Topological space.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Torus knot.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Trefoil knot.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Tubular neighborhood.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Underpinning.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Unknot.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Variable (mathematics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Whitehead link.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Wild knot.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Writhe.</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">Princeton Annals of Mathematics eBook-Package 1940-2020</subfield><subfield code="z">9783110494914</subfield><subfield code="o">ZDB-23-PMB</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">Princeton University Press eBook-Package Archive 1927-1999</subfield><subfield code="z">9783110442496</subfield></datafield><datafield tag="776" ind1="0" ind2=" "><subfield code="c">print</subfield><subfield code="z">9780691084350</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9781400882137</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://www.degruyter.com/isbn/9781400882137</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="3">Cover</subfield><subfield code="u">https://www.degruyter.com/document/cover/isbn/9781400882137/original</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">978-3-11-044249-6 Princeton University Press eBook-Package Archive 1927-1999</subfield><subfield code="c">1927</subfield><subfield code="d">1999</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_BACKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_CL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EBACKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ECL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EEBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ESTMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_PPALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_STMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV-deGruyter-alles</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA12STME</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA13ENGE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA18STMEE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA5EBK</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-PMB</subfield><subfield code="c">1940</subfield><subfield code="d">2020</subfield></datafield></record></collection> |