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035   $a(DE-B1597)9781400881420
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100   $a20190708d2016      fg              
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt
182   $cc
183   $acr
200 10$aBraids, Links, and Mapping Class Groups. (AM-82), Volume 82 /$fJoan S. Birman
210  1$aPrinceton, NJ : $cPrinceton University Press, $d[2016]
210  4$dİ1975
215   $a1 online resource (241 pages) $cillustrations
225 0 $aAnnals of Mathematics Studies ;$v238
300   $aIncludes index.
311   $a0-691-08149-2 
320   $aIncludes bibliographical references and index.
327   $tFrontmatter -- $tPREFACE -- $tTABLE OF CONTENTS -- $tCHAPTER 1. BRAID GROUPS -- $tCHAPTER 2. BRAIDS AND LINKS -- $tCHAPTER 3. MAGNUS REPRESENTATIONS -- $tCHAPTER 4. MAPPING CLASS GROUPS -- $tCHAPTER 5. PLATS AND LINKS -- $tAPPENDIX: RESEARCH PROBLEMS -- $tBIBLIOGRAPHY -- $tINDEX -- $tBackmatter
330   $aThe central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology.In Chapter 1 the author is concerned with the concept of a braid as a group of motions of points in a manifold. She studies structural and algebraic properties of the braid groups of two manifolds, and derives systems of defining relations for the braid groups of the plane and sphere. In Chapter 2 she focuses on the connections between the classical braid group and the classical knot problem. After reviewing basic results she proceeds to an exploration of some possible implications of the Garside and Markov theorems.Chapter 3 offers discussion of matrix representations of the free group and of subgroups of the automorphism group of the free group. These ideas come to a focus in the difficult open question of whether Burau's matrix representation of the braid group is faithful. Chapter 4 is a broad view of recent results on the connections between braid groups and mapping class groups of surfaces. Chapter 5 contains a brief discussion of the theory of "plats." Research problems are included in an appendix.
410  0$aAnnals of mathematics studies ;$vno. 82.
606   $aBraid theory
606   $aKnot theory
606   $aRepresentations of groups
610   $aAddition.
610   $aAlexander polynomial.
610   $aAlgebraic structure.
610   $aAutomorphism.
610   $aBall (mathematics).
610   $aBijection.
610   $aBraid group.
610   $aBraid theory.
610   $aBranched covering.
610   $aBurau representation.
610   $aCalculation.
610   $aCartesian coordinate system.
610   $aCharacterization (mathematics).
610   $aCoefficient.
610   $aCombinatorial group theory.
610   $aCommutative property.
610   $aCommutator subgroup.
610   $aConfiguration space.
610   $aConjugacy class.
610   $aCorollary.
610   $aCovering space.
610   $aDehn twist.
610   $aDeterminant.
610   $aDiagram (category theory).
610   $aDimension.
610   $aDisjoint union.
610   $aDouble coset.
610   $aEigenvalues and eigenvectors.
610   $aEnumeration.
610   $aEquation.
610   $aEquivalence class.
610   $aExact sequence.
610   $aExistential quantification.
610   $aFaithful representation.
610   $aFinite set.
610   $aFree abelian group.
610   $aFree group.
610   $aFundamental group.
610   $aGeometry.
610   $aGroup (mathematics).
610   $aGroup ring.
610   $aGroupoid.
610   $aHandlebody.
610   $aHeegaard splitting.
610   $aHomeomorphism.
610   $aHomomorphism.
610   $aHomotopy group.
610   $aHomotopy.
610   $aIdentity element.
610   $aIdentity matrix.
610   $aInclusion map.
610   $aInitial point.
610   $aInteger matrix.
610   $aInteger.
610   $aKnot polynomial.
610   $aKnot theory.
610   $aLens space.
610   $aLine segment.
610   $aLine?line intersection.
610   $aLink group.
610   $aLow-dimensional topology.
610   $aMapping class group.
610   $aMathematical induction.
610   $aMathematics.
610   $aMatrix group.
610   $aMatrix representation.
610   $aMonograph.
610   $aMorphism.
610   $aNatural transformation.
610   $aNormal matrix.
610   $aNotation.
610   $aOrientability.
610   $aParity (mathematics).
610   $aPermutation.
610   $aPiecewise linear.
610   $aPointwise.
610   $aPolynomial.
610   $aPrime knot.
610   $aProjection (mathematics).
610   $aProportionality (mathematics).
610   $aQuotient group.
610   $aRequirement.
610   $aRewriting.
610   $aRiemann surface.
610   $aSemigroup.
610   $aSequence.
610   $aSpecial case.
610   $aSubgroup.
610   $aSubmanifold.
610   $aSubset.
610   $aSymmetric group.
610   $aTheorem.
610   $aTheory.
610   $aTopology.
610   $aTrefoil knot.
610   $aTwo-dimensional space.
610   $aUnimodular matrix.
610   $aUnit vector.
610   $aVariable (mathematics).
610   $aWord problem (mathematics).
615  0$aBraid theory.
615  0$aKnot theory.
615  0$aRepresentations of groups.
676   $a514/.224
700   $aBirman$b Joan S., $0344665
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154753103321
996   $aBraids, Links, and Mapping Class Groups. (AM-82), Volume 82$92788037
997   $aUNINA