LEADER 04988nam 22007095 450 001 9910480431003321 005 20200702060652.0 010 $a1-4612-6869-9 010 $a1-4612-0691-X 024 7 $a10.1007/978-1-4612-0691-0 035 $a(CKB)3400000000089229 035 $a(SSID)ssj0000806845 035 $a(PQKBManifestationID)12426402 035 $a(PQKBTitleCode)TC0000806845 035 $a(PQKBWorkID)10750957 035 $a(PQKB)10460158 035 $a(SSID)ssj0001297217 035 $a(PQKBManifestationID)11858107 035 $a(PQKBTitleCode)TC0001297217 035 $a(PQKBWorkID)11363026 035 $a(PQKB)11527775 035 $a(DE-He213)978-1-4612-0691-0 035 $a(MiAaPQ)EBC3073377 035 $a(PPN)23800791X 035 $a(EXLCZ)993400000000089229 100 $a20121227d1997 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 13$aAn Introduction to Knot Theory$b[electronic resource] /$fby W.B.Raymond Lickorish 205 $a1st ed. 1997. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1997. 215 $a1 online resource (X, 204 p.) 225 1 $aGraduate Texts in Mathematics,$x0072-5285 ;$v175 300 $a"With 114 Illustrations." 311 $a0-387-98254-X 320 $aIncludes bibliographical references and index. 327 $a1. A Beginning for Knot Theory -- Exercises -- 2. Seifert Surfaces and Knot Factorisation -- Exercises -- 3. The Jones Polynomial -- Exercises -- 4. Geometry of Alternating Links -- Exercises -- 5. The Jones Polynomial of an Alternating Link -- Exercises -- 6. The Alexander Polynomial -- Exercises -- 7. Covering Spaces -- Exercises -- 8. The Conway Polynomial, Signatures and Slice Knots -- Exercises -- 9. Cyclic Branched Covers and the Goeritz Matrix -- Exercises -- 10. The Arf Invariant and the Jones Polynomia -- Exercises -- 11. The Fundamental Group -- Exercises -- 12. Obtaining 3-Manifolds by Surgery on S3 -- Exercises -- 13. 3-Manifold Invariants From The Jones Polynomial -- Exercises -- 14. Methods for Calculating Quantum Invariants -- Exercises -- 15. Generalisations of the Jones Polynomial -- Exercises -- 16. Exploring the HOMFLY and Kauffman Polynomials -- Exercises -- References. 330 $aThis account is an introduction to mathematical knot theory, the theory of knots and links of simple closed curves in three-dimensional space. Knots can be studied at many levels and from many points of view. They can be admired as artifacts of the decorative arts and crafts, or viewed as accessible intimations of a geometrical sophistication that may never be attained. The study of knots can be given some motivation in terms of applications in molecular biology or by reference to paral­ lels in equilibrium statistical mechanics or quantum field theory. Here, however, knot theory is considered as part of geometric topology. Motivation for such a topological study of knots is meant to come from a curiosity to know how the ge­ ometry of three-dimensional space can be explored by knotting phenomena using precise mathematics. The aim will be to find invariants that distinguish knots, to investigate geometric properties of knots and to see something of the way they interact with more adventurous three-dimensional topology. The book is based on an expanded version of notes for a course for recent graduates in mathematics given at the University of Cambridge; it is intended for others with a similar level of mathematical understanding. In particular, a knowledge of the very basic ideas of the fundamental group and of a simple homology theory is assumed; it is, after all, more important to know about those topics than about the intricacies of knot theory. 410 0$aGraduate Texts in Mathematics,$x0072-5285 ;$v175 606 $aManifolds (Mathematics) 606 $aComplex manifolds 606 $aGroup theory 606 $aMathematical physics 606 $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027 606 $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078 606 $aTheoretical, Mathematical and Computational Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19005 615 0$aManifolds (Mathematics). 615 0$aComplex manifolds. 615 0$aGroup theory. 615 0$aMathematical physics. 615 14$aManifolds and Cell Complexes (incl. Diff.Topology). 615 24$aGroup Theory and Generalizations. 615 24$aTheoretical, Mathematical and Computational Physics. 676 $a514/.224 700 $aLickorish$b W.B.Raymond$4aut$4http://id.loc.gov/vocabulary/relators/aut$0874453 906 $aBOOK 912 $a9910480431003321 996 $aAn Introduction to Knot Theory$91952520 997 $aUNINA