id sid eid entity type ejpam-1949 1 1 european journal ORG ejpam-1949 2 1 7 CARDINAL ejpam-1949 2 2 1, 2014 DATE ejpam-1949 2 3 65 CARDINAL ejpam-1949 2 4 mohamed maghfoul ORG ejpam-1949 2 5 ibn tofail university ORG ejpam-1949 2 6 kenitra GPE ejpam-1949 2 7 morocco GPE ejpam-1949 3 1 two CARDINAL ejpam-1949 4 1 six CARDINAL ejpam-1949 5 1 ǩ∗(ρ PERSON ejpam-1949 6 1 ǩ∗(ρ PERSON ejpam-1949 7 1 8 CARDINAL ejpam-1949 7 2 one CARDINAL ejpam-1949 8 1 2010 DATE ejpam-1949 8 2 19k33 CARDINAL ejpam-1949 8 3 51h25 CARDINAL ejpam-1949 8 4 1 CARDINAL ejpam-1949 9 1 5 CARDINAL ejpam-1949 10 1 topological ORG ejpam-1949 11 1 9 CARDINAL ejpam-1949 12 1 benameur PERSON ejpam-1949 12 2 maghfoul ORG ejpam-1949 12 3 2 CARDINAL ejpam-1949 13 1 cheeger-simons ORG ejpam-1949 13 2 baum-douglas ORG ejpam-1949 14 1 baum-douglas ORG ejpam-1949 15 1 c∗(x ORG ejpam-1949 16 1 1 CARDINAL ejpam-1949 17 1 c∗(x ORG ejpam-1949 18 1 h(∂w ORDINAL ejpam-1949 18 2 d(w PRODUCT ejpam-1949 19 1 ∗corresponding PERSON ejpam-1949 20 1 elmrabty_adnane@yahoo.fr (a. elmrabty ORG ejpam-1949 20 2 m. maghfoul PERSON ejpam-1949 21 1 65 CARDINAL ejpam-1949 22 1 2014 DATE ejpam-1949 23 1 a. elmrabty PERSON ejpam-1949 23 2 m. maghfoul PERSON ejpam-1949 24 1 j. pure PERSON ejpam-1949 24 2 7 (2014 DATE ejpam-1949 24 3 65 CARDINAL ejpam-1949 24 4 w ORG ejpam-1949 24 5 integer k-periods PERSON ejpam-1949 24 6 2 CARDINAL ejpam-1949 24 7 d(w GPE ejpam-1949 24 8 todd PERSON ejpam-1949 24 9 w GPE ejpam-1949 26 1 two CARDINAL ejpam-1949 28 1 8 CARDINAL ejpam-1949 29 1 section 2 LAW ejpam-1949 30 1 section 3 LAW ejpam-1949 31 1 two CARDINAL ejpam-1949 31 2 six CARDINAL ejpam-1949 32 1 section 4 LAW ejpam-1949 33 1 8 CARDINAL ejpam-1949 33 2 2 CARDINAL ejpam-1949 34 1 baum-douglas ORG ejpam-1949 35 1 1 CARDINAL ejpam-1949 36 1 1 CARDINAL ejpam-1949 39 1 • w GPE ejpam-1949 39 2 • CARDINAL ejpam-1949 39 3 • CARDINAL ejpam-1949 40 1 w GPE ejpam-1949 40 2 w. PERSON ejpam-1949 40 3 w ORG ejpam-1949 41 1 w tw PERSON ejpam-1949 41 2 ′,ε t ε′ DATE ejpam-1949 43 1 two CARDINAL ejpam-1949 43 2 w ORG ejpam-1949 43 3 • CARDINAL ejpam-1949 43 4 • CARDINAL ejpam-1949 43 5 a. elmrabty PERSON ejpam-1949 43 6 m. maghfoul PERSON ejpam-1949 44 1 j. pure PERSON ejpam-1949 44 2 7 (2014 DATE ejpam-1949 44 3 65-76 PERCENT ejpam-1949 47 1 w ORG ejpam-1949 47 2 w ORG ejpam-1949 48 1 abelian NORP ejpam-1949 52 1 1w CARDINAL ejpam-1949 52 2 1w CARDINAL ejpam-1949 54 1 tw ORG ejpam-1949 55 1 ⊕ GPE ejpam-1949 55 2 clifford modules over ORG ejpam-1949 57 1 two CARDINAL ejpam-1949 57 2 b0(h ORG ejpam-1949 57 3 s(h ORG ejpam-1949 57 4 b0(h)∪s(h PERSON ejpam-1949 58 1 two CARDINAL ejpam-1949 58 2 s(h ORG ejpam-1949 59 1 ⊗π∗ε PERSON ejpam-1949 60 1 ⊗π∗ε PERSON ejpam-1949 61 1 2 CARDINAL ejpam-1949 62 1 c∗(x ORG ejpam-1949 62 2 • CARDINAL ejpam-1949 62 3 • CARDINAL ejpam-1949 63 1 c∗(x ORG ejpam-1949 64 1 e′ DATE ejpam-1949 65 1 c∗(x ORG ejpam-1949 65 2 abelian NORP ejpam-1949 67 1 a. elmrabty PERSON ejpam-1949 67 2 m. maghfoul PERSON ejpam-1949 68 1 j. pure PERSON ejpam-1949 68 2 7 (2014 DATE ejpam-1949 68 3 65 CARDINAL ejpam-1949 68 4 68 CARDINAL ejpam-1949 71 1 c∗(x GPE ejpam-1949 73 1 bordism PERSON ejpam-1949 74 1 two CARDINAL ejpam-1949 74 2 w ORG ejpam-1949 74 3 two CARDINAL ejpam-1949 74 4 w ORG ejpam-1949 74 5 e′ DATE ejpam-1949 75 1 t m ′ DATE ejpam-1949 75 2 1 CARDINAL ejpam-1949 76 1 ∼b ORG ejpam-1949 76 2 c∗(x GPE ejpam-1949 77 1 c∗(x GPE ejpam-1949 78 1 abelian NORP ejpam-1949 79 1 abelian NORP ejpam-1949 79 2 abelian NORP ejpam-1949 84 1 3 CARDINAL ejpam-1949 85 1 c∗(x ORG ejpam-1949 85 2 k∗(x DATE ejpam-1949 86 1 k∗(x DATE ejpam-1949 86 2 ⊕ k1(x PERSON ejpam-1949 88 1 two CARDINAL ejpam-1949 88 2 ρ∗ PERSON ejpam-1949 88 3 k∗(x DATE ejpam-1949 88 4 abelian NORP ejpam-1949 91 1 k∗(ρ PERSON ejpam-1949 92 1 ρ∗ WORK_OF_ART ejpam-1949 95 1 ω∗(x CARDINAL ejpam-1949 96 1 ω∗(x CARDINAL ejpam-1949 97 1 d(w ORG ejpam-1949 98 1 d(w PRODUCT ejpam-1949 98 2 todd PERSON ejpam-1949 98 3 w GPE ejpam-1949 99 1 w ∈ PRODUCT ejpam-1949 99 2 m. maghfoul PERSON ejpam-1949 100 1 j. pure PERSON ejpam-1949 100 2 7 (2014 DATE ejpam-1949 100 3 65 CARDINAL ejpam-1949 100 4 r. NORP ejpam-1949 100 5 abelian NORP ejpam-1949 100 6 integer k-periods PERSON ejpam-1949 100 7 ω∗0(x ORG ejpam-1949 102 1 0 CARDINAL ejpam-1949 104 1 1 CARDINAL ejpam-1949 106 1 integer k-periods PERSON ejpam-1949 106 2 e⊗ GPE ejpam-1949 107 1 ⊗ f PERSON ejpam-1949 109 1 4 DATE ejpam-1949 111 1 c∗(x ORG ejpam-1949 111 2 w ORG ejpam-1949 112 1 d(w PRODUCT ejpam-1949 113 1 w ORG ejpam-1949 113 2 integer k-periods PERSON ejpam-1949 114 1 k̂∗(x ORG ejpam-1949 115 1 abelian NORP ejpam-1949 115 2 = k̂0(x PERSON ejpam-1949 115 3 ⊕ k̂1(x PERSON ejpam-1949 116 1 w ORG ejpam-1949 119 1 ω∗(x PRODUCT ejpam-1949 119 2 fϕv(m ORG ejpam-1949 122 1 mod z. PERSON ejpam-1949 122 2 δ0(fϕv ORG ejpam-1949 125 1 0→ CARDINAL ejpam-1949 125 2 0 CARDINAL ejpam-1949 126 1 k̂1(pt)∼= z. a. elmrabty PERSON ejpam-1949 126 2 m. maghfoul PERSON ejpam-1949 127 1 j. pure PERSON ejpam-1949 127 2 7 (2014 DATE ejpam-1949 127 3 65 CARDINAL ejpam-1949 128 1 two CARDINAL ejpam-1949 128 2 ρ∗ PRODUCT ejpam-1949 128 3 k̂∗(y GPE ejpam-1949 128 4 abelian NORP ejpam-1949 129 1 h(ρ∗(m CARDINAL ejpam-1949 129 2 c∗(x ORG ejpam-1949 135 1 0→ CARDINAL ejpam-1949 136 1 0 CARDINAL ejpam-1949 136 2 isomorphisms k̂0(x PERSON ejpam-1949 136 3 k̂1(x PERSON ejpam-1949 137 1 3 CARDINAL ejpam-1949 137 2 two CARDINAL ejpam-1949 137 3 six CARDINAL ejpam-1949 140 1 l∗(x DATE ejpam-1949 140 2 l∗(x DATE ejpam-1949 141 1 abelian NORP ejpam-1949 141 2 l∗(x DATE ejpam-1949 142 1 w ORG ejpam-1949 144 1 w GPE ejpam-1949 145 1 two CARDINAL ejpam-1949 150 1 b̌∗(ρ PERSON ejpam-1949 151 1 a. elmrabty PERSON ejpam-1949 151 2 m. maghfoul PERSON ejpam-1949 152 1 j. pure PERSON ejpam-1949 152 2 7 (2014 DATE ejpam-1949 152 3 65 CARDINAL ejpam-1949 152 4 5 CARDINAL ejpam-1949 153 1 ž∗(ρ)/b̌∗(ρ ORG ejpam-1949 155 1 ρ′ DATE ejpam-1949 155 2 ǩ∗(ρ)→ ǩ∗(ρ′ PERSON ejpam-1949 155 3 abelian NORP ejpam-1949 155 4 g)∗([s ORG ejpam-1949 158 1 cx ORG ejpam-1949 158 2 wx PERSON ejpam-1949 158 3 cy PERSON ejpam-1949 159 1 0 CARDINAL ejpam-1949 162 1 ρ∗cx CARDINAL ejpam-1949 164 1 ρ∗hx CARDINAL ejpam-1949 164 2 0 CARDINAL ejpam-1949 166 1 j(s GPE ejpam-1949 169 1 0 CARDINAL ejpam-1949 170 1 j. now PERSON ejpam-1949 171 1 h′ = h. ORG ejpam-1949 172 1 ϕδ0(h)−δh′. PERSON ejpam-1949 175 1 0 CARDINAL ejpam-1949 176 1 0 CARDINAL ejpam-1949 177 1 0 CARDINAL ejpam-1949 177 2 h′′ PERSON ejpam-1949 178 1 h′′ PERSON ejpam-1949 178 2 ∈ l∗(y ORG ejpam-1949 178 3 γ ∈ l∗−1(y ORG ejpam-1949 179 1 h′′,δ0(h PERSON ejpam-1949 180 1 0 CARDINAL ejpam-1949 180 2 0 DATE ejpam-1949 181 1 k̂∗(y GPE ejpam-1949 181 2 θ(h PERSON ejpam-1949 183 1 0 CARDINAL ejpam-1949 184 1 a. elmrabty PERSON ejpam-1949 184 2 m. maghfoul PERSON ejpam-1949 185 1 j. pure PERSON ejpam-1949 185 2 7 (2014 DATE ejpam-1949 185 3 65 CARDINAL ejpam-1949 185 4 1 CARDINAL ejpam-1949 186 1 six CARDINAL ejpam-1949 186 2 k̂0(x GPE ejpam-1949 186 3 ρ∗ // k̂0(y PERSON ejpam-1949 186 4 θ // ǩ0(ρ PERSON ejpam-1949 186 5 j �� ǩ1(ρ PERSON ejpam-1949 186 6 k̂1(y PERSON ejpam-1949 186 7 k̂1(x PERSON ejpam-1949 186 8 ρ∗oo PERSON ejpam-1949 190 1 cx ORG ejpam-1949 190 2 wx PERSON ejpam-1949 191 1 cy PERSON ejpam-1949 192 1 0 CARDINAL ejpam-1949 193 1 wx ORG ejpam-1949 193 2 0 CARDINAL ejpam-1949 193 3 cx ORG ejpam-1949 193 4 ∈ ORG ejpam-1949 194 1 0 CARDINAL ejpam-1949 194 2 cy ORG ejpam-1949 195 1 0 DATE ejpam-1949 195 2 0 CARDINAL ejpam-1949 195 3 cy ORG ejpam-1949 196 1 k̂1(x PERSON ejpam-1949 197 1 cx ORG ejpam-1949 197 2 wx PERSON ejpam-1949 197 3 cy ORG ejpam-1949 198 1 0 CARDINAL ejpam-1949 198 2 ∈ ORG ejpam-1949 199 1 ρ∗ ORG ejpam-1949 199 2 j[s DATE ejpam-1949 202 1 first ORDINAL ejpam-1949 203 1 0 CARDINAL ejpam-1949 204 1 ∈ ORG ejpam-1949 204 2 l1(y GPE ejpam-1949 205 1 0 DATE ejpam-1949 209 1 0 CARDINAL ejpam-1949 209 2 ρ ∗h′,ρ∗δ0(h GPE ejpam-1949 214 1 cx ORG ejpam-1949 214 2 wx PERSON ejpam-1949 214 3 cy ORG ejpam-1949 215 1 0 CARDINAL ejpam-1949 219 1 ρ∗cx ORG ejpam-1949 223 1 wx PERSON ejpam-1949 223 2 ρ∗(hx DATE ejpam-1949 225 1 1 CARDINAL ejpam-1949 228 1 ǩ∗(i)→ k̂∗−1(x PERSON ejpam-1949 229 1 k̃∗−1(x PERSON ejpam-1949 230 1 a. elmrabty PERSON ejpam-1949 230 2 m. maghfoul PERSON ejpam-1949 231 1 j. pure PERSON ejpam-1949 231 2 7 (2014 DATE ejpam-1949 231 3 65-76 73 PERCENT ejpam-1949 233 1 8 CARDINAL ejpam-1949 233 2 two CARDINAL ejpam-1949 234 1 cx ORG ejpam-1949 234 2 0 DATE ejpam-1949 234 3 0 DATE ejpam-1949 235 1 abelian NORP ejpam-1949 238 1 6 CARDINAL ejpam-1949 240 1 abelian NORP ejpam-1949 241 1 six CARDINAL ejpam-1949 241 2 section 3: LAW ejpam-1949 241 3 ρ∗ // k̂0(y PERSON ejpam-1949 241 4 θ // ǩ0(ρ PERSON ejpam-1949 241 5 j �� ǩ1(ρ PERSON ejpam-1949 241 6 k̂1(y PERSON ejpam-1949 241 7 k̂1(x PERSON ejpam-1949 244 1 ǩ∗(ρ GPE ejpam-1949 245 1 k∗(x DATE ejpam-1949 246 1 six CARDINAL ejpam-1949 246 2 ρ∗ // PERSON ejpam-1949 246 3 θ // ǩ0(ρ PERSON ejpam-1949 246 4 j �� ǩ1(ρ PERSON ejpam-1949 246 5 j oo k1(y PERSON ejpam-1949 246 6 k∗(x DATE ejpam-1949 246 7 2 CARDINAL ejpam-1949 247 1 k∗(ρ PERSON ejpam-1949 248 1 8 CARDINAL ejpam-1949 248 2 k∗(ρ PERSON ejpam-1949 248 3 8 CARDINAL ejpam-1949 249 1 l∗(ρ PERSON ejpam-1949 250 1 a. elmrabty PERSON ejpam-1949 250 2 m. maghfoul PERSON ejpam-1949 251 1 j. pure PERSON ejpam-1949 251 2 7 (2014 DATE ejpam-1949 251 3 65 CARDINAL ejpam-1949 252 1 ∂̂ LANGUAGE ejpam-1949 252 2 α+ρ∗β ORG ejpam-1949 253 1 ∂̂ NORP ejpam-1949 255 1 αtα′,β GPE ejpam-1949 256 1 bordism PERSON ejpam-1949 257 1 two CARDINAL ejpam-1949 257 2 σ ORG ejpam-1949 258 1 σ ORG ejpam-1949 259 1 7 CARDINAL ejpam-1949 260 1 k∗(ρ PERSON ejpam-1949 261 1 k∗(ρ PERSON ejpam-1949 261 2 ž∗(ρ GPE ejpam-1949 262 1 cx ORG ejpam-1949 262 2 0 DATE ejpam-1949 262 3 0 DATE ejpam-1949 263 1 ∈ ORG ejpam-1949 264 1 cx ORG ejpam-1949 264 2 0 DATE ejpam-1949 264 3 0 DATE ejpam-1949 264 4 σ ORG ejpam-1949 264 5 µ(s DATE ejpam-1949 264 6 ∂̂ NORP ejpam-1949 264 7 σ ORG ejpam-1949 265 1 σ+ρ∗τ,−∂ ORG ejpam-1949 265 2 fhx(∂ σ PERSON ejpam-1949 266 1 àρ∗hx ORG ejpam-1949 266 2 σ ORG ejpam-1949 267 1 ǩ∗(ρ PERSON ejpam-1949 267 2 1 CARDINAL ejpam-1949 270 1 six CARDINAL ejpam-1949 270 2 8 CARDINAL ejpam-1949 270 3 8 CARDINAL ejpam-1949 271 1 ζ // k1(x PERSON ejpam-1949 271 2 ρ∗ // k1(y PERSON ejpam-1949 271 3 ρ∗oo k̂0(ρ PERSON ejpam-1949 271 4 75 CARDINAL ejpam-1949 271 5 six CARDINAL ejpam-1949 271 6 1 CARDINAL ejpam-1949 271 7 ρ∗ // PERSON ejpam-1949 271 8 θ // ǩ0(ρ PERSON ejpam-1949 272 1 j gg PERSON ejpam-1949 273 1 ρ∗ // PERSON ejpam-1949 274 1 // PERSON ejpam-1949 274 2 ζ gg k1(y PERSON ejpam-1949 275 1 five CARDINAL ejpam-1949 277 1 1 CARDINAL ejpam-1949 277 2 g douglas PERSON ejpam-1949 279 1 algebras ORG ejpam-1949 280 1 38 CARDINAL ejpam-1949 280 2 117–173 CARDINAL ejpam-1949 280 3 kingston GPE ejpam-1949 280 4 ontario GPE ejpam-1949 280 5 1982 DATE ejpam-1949 281 1 american mathematical society ORG ejpam-1949 282 1 2 CARDINAL ejpam-1949 284 1 24:417–432 CARDINAL ejpam-1949 284 2 2006 DATE ejpam-1949 285 1 3 CARDINAL ejpam-1949 285 2 t schick LOC ejpam-1949 286 1 smooth k-theory PERSON ejpam-1949 287 1 328:45–135 CARDINAL ejpam-1949 287 2 2009 DATE ejpam-1949 288 1 4 CARDINAL ejpam-1949 288 2 t schick LOC ejpam-1949 292 1 17 CARDINAL ejpam-1949 292 2 303–358 CARDINAL ejpam-1949 292 3 heidelberg GPE ejpam-1949 292 4 2012 DATE ejpam-1949 293 1 5 CARDINAL ejpam-1949 293 2 j hopkins PERSON ejpam-1949 295 1 5(44 CARDINAL ejpam-1949 295 2 2000 DATE ejpam-1949 296 1 6 CARDINAL ejpam-1949 296 2 j lott PERSON ejpam-1949 298 1 14:903–966 CARDINAL ejpam-1949 298 2 2010 DATE ejpam-1949 299 1 7 CARDINAL ejpam-1949 299 2 j lott PERSON ejpam-1949 301 1 2(2):279–311 CARDINAL ejpam-1949 301 2 1994 DATE ejpam-1949 302 1 8 CARDINAL ejpam-1949 304 1 2008 DATE ejpam-1949 305 1 76 CARDINAL ejpam-1949 306 1 9 CARDINAL ejpam-1949 306 2 j simons PERSON ejpam-1949 308 1 quanta of maths ORG ejpam-1949 309 1 11 CARDINAL ejpam-1949 309 2 579–599 CARDINAL ejpam-1949 310 1 american mathematical society ORG ejpam-1949 310 2 2010 DATE