| Preface |
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xi | |
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1 | (140) |
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3 | (24) |
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3 | (2) |
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5 | (5) |
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1.3 Homology boundary links |
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10 | (1) |
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11 | (2) |
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1.5 Isotopy, concordance and I-equivalence |
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13 | (3) |
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1.6 Link homotopy and surgery |
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16 | (2) |
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18 | (6) |
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1.8 Link-symmetric groups |
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24 | (1) |
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25 | (2) |
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Chapter 2 Homology and Duality in Covers |
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27 | (20) |
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2.1 Homology and cohomology with local coefficients |
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27 | (1) |
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2.2 Covers of link exteriors |
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28 | (2) |
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2.3 Some terminology and notation |
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30 | (1) |
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2.4 Poincare duality and the Blanchfield pairings |
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30 | (3) |
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2.5 The total linking number cover |
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33 | (2) |
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2.6 The maximal abelian cover |
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35 | (1) |
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36 | (2) |
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38 | (2) |
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40 | (2) |
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42 | (5) |
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Chapter 3 Determinantal Invariants |
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47 | (22) |
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47 | (7) |
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3.2 The Elementary Divisor Theorem |
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54 | (2) |
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56 | (3) |
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3.4 Reidemeister-Franz torsion |
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59 | (2) |
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3.5 Steinitz-Fox-Smythe invariants |
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61 | (2) |
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3.6 1- and 2-dimensional rings |
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63 | (3) |
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66 | (3) |
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Chapter 4 The Maximal Abelian Cover |
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69 | (26) |
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4.1 Metabelian groups and the Crowell sequence |
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69 | (2) |
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4.2 Free metabelian groups |
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71 | (2) |
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4.3 Link module sequences |
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73 | (3) |
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4.4 Localization of link module sequences |
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76 | (2) |
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78 | (1) |
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4.6 Applications to links |
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78 | (5) |
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4.7 Chen groups, nullity and longitudes |
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83 | (4) |
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87 | (2) |
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4.9 The sign-determined Alexander polynomial |
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89 | (2) |
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4.10 Higher dimensional links |
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91 | (4) |
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Chapter 5 Sublinks and Other Abelian Covers |
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95 | (30) |
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5.1 The Torres conditions |
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95 | (5) |
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100 | (3) |
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103 | (2) |
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5.4 The total linking number cover |
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105 | (3) |
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108 | (2) |
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110 | (3) |
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5.7 Finite abelian covers |
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113 | (6) |
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5.8 Cyclic branched covers |
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119 | (3) |
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5.9 Families of coverings |
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122 | (3) |
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Chapter 6 Twisted Polynomial Invariants |
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125 | (16) |
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6.1 Definition in terms of local coefficients |
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125 | (2) |
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127 | (2) |
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6.3 Reidemeister-Franz torsion |
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129 | (1) |
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130 | (2) |
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132 | (4) |
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136 | (5) |
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Part 2 Applications: Special Cases and Symmetries |
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141 | (106) |
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143 | (24) |
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143 | (2) |
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145 | (2) |
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147 | (3) |
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7.4 Recovering the module from the polynomial |
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150 | (2) |
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7.5 Homogeneity and realizing π-primary sequences |
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152 | (2) |
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7.6 The Blanchfield pairing |
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154 | (5) |
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7.7 Blanchfield pairings and Seifert matrices |
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159 | (2) |
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161 | (2) |
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7.9 Alexander polynomials of ribbon links |
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163 | (4) |
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Chapter 8 Links with Two Components |
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167 | (22) |
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167 | (5) |
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8.2 Consequences of Bailey's Theorem |
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172 | (4) |
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8.3 The Blanchfield pairing |
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176 | (2) |
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8.4 Links with Alexander polynomial 0 |
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178 | (3) |
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8.5 2-Component Z/2Z-boundary links |
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181 | (2) |
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8.6 Topological concordance and F-isotopy |
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183 | (1) |
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184 | (5) |
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189 | (30) |
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189 | (1) |
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9.2 Symmetries of knot types |
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190 | (6) |
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9.3 Group actions on links |
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196 | (1) |
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197 | (2) |
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9.5 Semifree periods - the Murasugi conditions |
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199 | (6) |
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9.6 Semifree periods and splitting fields |
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205 | (3) |
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9.7 Links with infinitely many semifree periods |
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208 | (4) |
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9.8 Knots with free periods |
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212 | (3) |
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9.9 Equivariant concordance |
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215 | (4) |
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Chapter 10 Singularities of Plane Algebraic Curves |
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219 | (28) |
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219 | (3) |
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222 | (4) |
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226 | (4) |
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230 | (4) |
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234 | (5) |
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10.6 Resolution of singularities |
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239 | (1) |
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10.7 The Gauß-Manin connection |
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240 | (2) |
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10.8 The weighted homogeneous case |
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242 | (3) |
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10.9 An hermitean pairing |
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245 | (2) |
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Part 3 Free Covers, Nilpotent Quotients and Completion |
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247 | (76) |
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249 | (24) |
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249 | (2) |
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251 | (6) |
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257 | (2) |
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11.4 The Farber derivations |
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259 | (1) |
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11.5 The maximal free cover and duality |
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260 | (4) |
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264 | (2) |
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266 | (1) |
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11.8 An unlinking theorem |
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266 | (2) |
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11.9 Patterns and calibrations |
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268 | (2) |
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270 | (3) |
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Chapter 12 Nilpotent Quotients |
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273 | (20) |
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273 | (2) |
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12.2 Products, the Dwyer filtration and gropes |
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275 | (2) |
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277 | (1) |
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12.4 The graded Lie algebra of a group |
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278 | (1) |
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12.5 DGAs and minimal models |
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279 | (3) |
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282 | (1) |
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283 | (5) |
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12.8 Link homotopy and the Milnor group |
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288 | (2) |
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12.9 Variants of the Milnor invariants |
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290 | (1) |
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12.10 Solvable quotients and covering spaces |
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291 | (2) |
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Chapter 13 Algebraic Closure |
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293 | (14) |
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13.1 Homological localization |
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293 | (1) |
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13.2 The nilpotent completion of a group |
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294 | (1) |
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13.3 The algebraic closure of a group |
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295 | (6) |
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301 | (2) |
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13.5 Other notions of closure |
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303 | (1) |
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13.6 Orr invariants and cSHB-links |
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304 | (3) |
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307 | (16) |
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14.1 Disc links and string links |
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307 | (2) |
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309 | (1) |
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14.3 Concordance and the Artin representation |
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310 | (4) |
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314 | (1) |
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14.5 Milnor invariants again |
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315 | (1) |
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14.6 The Gassner representation |
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316 | (3) |
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319 | (4) |
| Bibliography |
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323 | (24) |
| Index |
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347 | |
Rohkem infot World Scientific e-raamatute kohta