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035   $a(OCoLC)979728851
035   $a(DE-B1597)9781400882137
035   $a(EXLCZ)993710000000620163
100   $a20190708d2016      fg              
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt
182   $cc
183   $acr
200 10$aOn Knots. (AM-115), Volume 115 /$fLouis H. Kauffman
210  1$aPrinceton, NJ : $cPrinceton University Press, $d[2016]
210  4$dİ2016
215   $a1 online resource (497 pages) $cillustrations
225 0 $aAnnals of Mathematics Studies ;$v121
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a0-691-08435-1 
311   $a0-691-08434-3 
320   $aBibliography.
327   $tFrontmatter -- $tCONTENTS -- $tPREFACE -- $tI. INTRODUCTION -- $tII. LINKING NUMBERS AND REIDEMEISTER MOVES -- $tIII. THE CONWAY POLYNOMIAL -- $tIV. EXAMPLE S AND SKEIN THEORY -- $tV. DETECTING SLICES AND RIBBONS- A FIRST PASS -- $tVI. MISCELLANY -- $tVII. SPANNING SURFACES AND THE SEIFERT PAIRING -- $tVIII. RIBBONS AND SLICES -- $tIX. THE ALEXANDER POLYNOMIAL AND BRANCHED COVERINGS -- $tX. THE ALEXANDER POLYNOMIAL AND THE ARF INVARIANT -- $tXI. FREE DIFFERENTIAL CALCULUS -- $tXII. CYCLIC BRANCHED COVERINGS -- $tXIII. SIGNATURE THEOREMS -- $tXIV. G-SIGNATURE THEOREM FOR FOUR MANIFOLDS -- $tXV. SIGNATURE OF CYCLIC BRANCHED COVERINGS -- $tXVI. AN INVARIANT FOR COVERINGS -- $tXVII. SLICE KNOTS -- $tXVIII. CALCULATING ?r FOR GENERALIZED STEVEDORE'S KNOT -- $tXIX. SINGULARITIES, KNOTS AND BRIESKORN VARIETIES -- $tAPPENDIX. GENERALIZED POLYNOMIALS AND A STATE MODEL FOR THE JONES POLYNOMIAL -- $tKNOT TABLES AND THE L-POLYNOMIAL -- $tREFERENCES
330   $aOn Knots is a journey through the theory of knots, starting from the simplest combinatorial ideas--ideas arising from the representation of weaving patterns. From this beginning, topological invariants are constructed directly: first linking numbers, then the Conway polynomial and skein theory. This paves the way for later discussion of the recently discovered Jones and generalized polynomials. The central chapter, Chapter Six, is a miscellany of topics and recreations. Here the reader will find the quaternions and the belt trick, a devilish rope trick, Alhambra mosaics, Fibonacci trees, the topology of DNA, and the author's geometric interpretation of the generalized Jones Polynomial.Then come branched covering spaces, the Alexander polynomial, signature theorems, the work of Casson and Gordon on slice knots, and a chapter on knots and algebraic singularities.The book concludes with an appendix about generalized polynomials.
410  0$aAnnals of mathematics studies ;$vno. 115.
606   $aKnot theory
610   $a3-sphere.
610   $aAddition theorem.
610   $aAddition.
610   $aAlexander polynomial.
610   $aAlgebraic variety.
610   $aAlgorithm.
610   $aAmbient isotopy.
610   $aArf invariant.
610   $aBasepoint.
610   $aBijection.
610   $aBilinear form.
610   $aBorromean rings.
610   $aBracket polynomial.
610   $aBraid group.
610   $aBranched covering.
610   $aChiral knot.
610   $aChromatic polynomial.
610   $aCobordism.
610   $aCodimension.
610   $aCombination.
610   $aCombinatorics.
610   $aComplex analysis.
610   $aConcentric.
610   $aConjecture.
610   $aConnected sum.
610   $aConway polynomial (finite fields).
610   $aCounting.
610   $aCovering space.
610   $aCyclic group.
610   $aDense set.
610   $aDeterminant.
610   $aDiagram (category theory).
610   $aDiffeomorphism.
610   $aDimension.
610   $aDisjoint union.
610   $aDisk (mathematics).
610   $aDual graph.
610   $aElementary algebra.
610   $aEmbedding.
610   $aEnumeration.
610   $aExistential quantification.
610   $aExotic sphere.
610   $aFibration.
610   $aFormal power series.
610   $aFundamental group.
610   $aGeometric topology.
610   $aGeometry and topology.
610   $aGeometry.
610   $aGroup action.
610   $aHomotopy.
610   $aInteger.
610   $aIntersection form (4-manifold).
610   $aIsolated singularity.
610   $aJones polynomial.
610   $aKnot complement.
610   $aKnot group.
610   $aKnot theory.
610   $aLaws of Form.
610   $aLens space.
610   $aLinking number.
610   $aManifold.
610   $aModule (mathematics).
610   $aMorwen Thistlethwaite.
610   $aNormal bundle.
610   $aNotation.
610   $aObstruction theory.
610   $aOperator algebra.
610   $aPairing.
610   $aParity (mathematics).
610   $aPartition function (mathematics).
610   $aPlanar graph.
610   $aPoint at infinity.
610   $aPolynomial ring.
610   $aPolynomial.
610   $aQuantity.
610   $aRectangle.
610   $aReidemeister move.
610   $aRemainder.
610   $aRoot of unity.
610   $aSaddle point.
610   $aSeifert surface.
610   $aSingularity theory.
610   $aSlice knot.
610   $aSpecial case.
610   $aStatistical mechanics.
610   $aSubstructure.
610   $aSummation.
610   $aSymmetry.
610   $aTheorem.
610   $aThree-dimensional space (mathematics).
610   $aTopological space.
610   $aTorus knot.
610   $aTrefoil knot.
610   $aTubular neighborhood.
610   $aUnderpinning.
610   $aUnknot.
610   $aVariable (mathematics).
610   $aWhitehead link.
610   $aWild knot.
610   $aWrithe.
615  0$aKnot theory.
676   $a514/.224
700   $aKauffman$b Louis H., $057757
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154751303321
996   $aOn Knots. (AM-115), Volume 115$92785795
997   $aUNINA