LEADER 05120nam 2200673 a 450 001 9910826514503321 005 20240404143407.0 010 $a981-277-664-8 035 $a(CKB)1000000000414877 035 $a(EBL)1679572 035 $a(OCoLC)879023793 035 $a(SSID)ssj0000101034 035 $a(PQKBManifestationID)11125079 035 $a(PQKBTitleCode)TC0000101034 035 $a(PQKBWorkID)10060131 035 $a(PQKB)11258497 035 $a(MiAaPQ)EBC1679572 035 $a(WSP)00005091 035 $a(Au-PeEL)EBL1679572 035 $a(CaPaEBR)ebr10201145 035 $a(CaONFJC)MIL505385 035 $a(EXLCZ)991000000000414877 100 $a20030328d2002 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAlgebraic invariants of links /$fJonathan Hillman 205 $a1st ed. 210 $aRiver Edge, NJ $cWorld Scientific$dc2002 215 $a1 online resource (321 p.) 225 1 $aK & E series on knots and everything ;$vv. 32 300 $aDescription based upon print version of record. 311 $a981-238-154-6 320 $aIncludes bibliography (p. 277-298) and index. 327 $aContents ; Preface ; Part 1. Abelian Covers ; Chapter 1. Links ; 1.1. Basic notions ; 1.2. The link group ; 1.3. Homology boundary links ; 1.4. Z/2Z-boundary links ; 1.5. Isotopy concordance and /-equivalence ; 1.6. Link homotopy and surgery ; 1.7. Ribbon links 327 $a1.8. Link-symmetric groups 1.9. Link composition ; Chapter 2. Homology and Duality in Covers ; 2.1. Homology and cohomology with local coefficients ; 2.2. Covers of link exteriors ; 2.3. Poincare duality and the Blanchfield pairings ; 2.4. The total linking number cover 327 $a2.5. The maximal abelian cover 2.6. Concordance ; 2.7. Additivity ; 2.8. The Seifert approach for boundary 1-links ; 2.9. Signatures ; Chapter 3. Determinantal Invariants ; 3.1. Elementary ideals ; 3.2. The Elementary Divisor Theorem ; 3.3. Extensions 327 $a3.4. Reidemeister-Franz torsion 3.5. Steinitz-Fox-Smythe invariants ; 3.6. 1- and 2-dimensional rings ; 3.7. Bilinear pairings ; Chapter 4. The Maximal Abelian Cover ; 4.1. Metabelian groups and the Crowell sequence ; 4.2. Free metabelian groups ; 4.3. Link module sequences 327 $a4.4. Localization of link module sequences 4.5. Chen groups ; 4.6. Applications to links ; 4.7. Chen groups nullity and longitudes ; 4.8. I-equivalence ; 4.9. The sign-determined Alexander polynomial ; 4.10. Higher dimensional links ; Chapter 5. Sublinks and Other Abelian Covers 327 $a5.1. The Torres conditions 330 $a This book is intended as a reference on links and on the invariants derived via algebraic topology from covering spaces of link exteriors. It emphasizes features of the multicomponent case not normally considered by knot theorists, such as longitudes, the homological complexity of many-variable Laurent polynomial rings, free coverings of homology boundary links, the fact that links are not usually boundary links, the lower central series as a source of invariants, nilpotent completion and algebraic closure of the link group, and disc links. Invariants of the types considered here play an esse 410 0$aK & E series on knots and everything ;$vv. 32. 606 $aLink theory 606 $aInvariants 606 $aAbelian groups 615 0$aLink theory. 615 0$aInvariants. 615 0$aAbelian groups. 676 $a514.224 700 $aHillman$b Jonathan A$g(Jonathan Arthur),$f1947-$060427 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910826514503321 996 $aAlgebraic invariants of links$93944185 997 $aUNINA