LEADER 04319nam 2200685 450 001 9910453774803321 005 20200903223051.0 010 $a3-11-027078-1 024 7 $a10.1515/9783110270785 035 $a(CKB)2550000001169784 035 $a(EBL)1130364 035 $a(OCoLC)865329956 035 $a(SSID)ssj0001061240 035 $a(PQKBManifestationID)11695241 035 $a(PQKBTitleCode)TC0001061240 035 $a(PQKBWorkID)11098243 035 $a(PQKB)10778301 035 $a(MiAaPQ)EBC1130364 035 $a(DE-B1597)173980 035 $a(OCoLC)864432644 035 $a(OCoLC)988560843 035 $a(DE-B1597)9783110270785 035 $a(PPN)18293814X 035 $a(Au-PeEL)EBL1130364 035 $a(CaPaEBR)ebr10820052 035 $a(CaONFJC)MIL551769 035 $a(EXLCZ)992550000001169784 100 $a20131030d2013 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aKnots /$fGerhard Burde, Heiner Zieschang, Michael Heusener 205 $aThird, fully revised and extended edition. 210 1$aBerlin ;$aBoston :$cWalter de Gruyter GmbH & Co. KG,$d2013. 215 $a1 online resource (432 p.) 225 0 $aDe Gruyter Studies in Mathematics ;$v5 225 0$aDe Gruyter studies in mathematics,$x0179-0986 ;$v5 300 $aDescription based upon print version of record. 311 $a3-11-027074-9 311 $a1-306-20518-2 320 $aIncludes bibliographical references and indexes. 327 $t Frontmatter -- $tPreface to the First Edition -- $tPreface to the Second Edition -- $tPreface to the Third Edition -- $tContents -- $tChapter 1: Knots and isotopies -- $tChapter 2: Geometric concepts -- $tChapter 3: Knot groups -- $tChapter 4: Commutator subgroup of a knot group -- $tChapter 5: Fibered knots -- $tChapter 6: A characterization of torus knots -- $tChapter 7: Factorization of knots -- $tChapter 8: Cyclic coverings and Alexander invariants -- $tChapter 9: Free differential calculus and Alexander matrices -- $tChapter 10: Braids -- $tChapter 11: Manifolds as branched coverings -- $tChapter 12: Montesinos links -- $tChapter 13: Quadratic forms of a knot -- $tChapter 14: Representations of knot groups -- $tChapter 15: Knots, knot manifolds, and knot groups -- $tChapter 16: Bridge number and companionship -- $tChapter 17: The 2-variable skein polynomial -- $tAppendix A: Algebraic theorems -- $tAppendix B: Theorems of 3-dimensional topology -- $tAppendix C: Table -- $tAppendix D: Knot projections 01-949 -- $tReferences -- $tAuthor index -- $tGlossary of Symbols -- $tIndex 330 $aThis book is an introduction to classical knot theory. Topics covered include: different constructions of knots, knot diagrams, knot groups, fibred knots, characterisation of torus knots, prime decomposition of knots, cyclic coverings and Alexander polynomials and modules together with the free differential calculus, braids, branched coverings and knots, Montesinos links, representations of knot groups, surgery of 3-manifolds and knots, Jones and HOMFLYPT polynomials. Knot theory has expanded enormously since the first edition of this book published in 1985. In this third completely revised and extended edition a chapter about bridge number and companionship of knots has been added. The book contains many figures and some tables of invariants of knots. This comprehensive account is an indispensable reference source for anyone interested in both classical and modern knot theory. Most of the topics considered in the book are developed in detail; only the main properties of fundamental groups, covering spaces and some basic results of combinatorial group theory are assumed to be known. The text is accessible to advanced undergraduate and graduate students in mathematics. 410 3$aDe Gruyter Studies in Mathematics 606 $aKnot theory 608 $aElectronic books. 615 0$aKnot theory. 676 $a514/.2242 700 $aBurde$b Gerhard$f1931-$0535866 701 $aZieschang$b Heiner$055310 701 $aHeusener$b Michael$0740886 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910453774803321 996 $aKnots$91469700 997 $aUNINA