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Localization of a topological space

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is a geometric form of the algebraic device of choosing 'coefficients' in order to simplify the algebra, in a given problem. Instead of that, the localization can be applied to the space
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Geometric Topology: Localization, Periodicity and Galois Symmetry: The 1970 MIT Notes
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The reason to do this was in line with an idea of making
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in 1970 lecture notes that were finally published in (
320:, K-Monographs in Mathematics, Dordrecht: Springer, 146:is universal for (homotopy classes of) maps from 43:at a prime. This construction was described by 105:. Then there is a simply connected CW complex 378: 8: 385: 371: 62:, more geometric. Localization of a space 48: 232:to the homology and homotopy groups of 7: 339: 337: 245:Category:Localization (mathematics) 39:at primes, in a similar way to the 70:, directly, giving a second space 25: 341: 128:-local; this means that all its 1: 357:. You can help Knowledge by 430: 409:Localization (mathematics) 336: 256:Localization of a category 414:Commutative algebra stubs 109:together with a map from 261:Localization of a module 185:is the localization of 353:-related article is a 271:Bousfield localization 266:Localization of a ring 41:localization of a ring 288:Infinite loop spaces 166:, and is called the 164:homotopy equivalence 154:-local CW complexes. 351:commutative algebra 305:Sullivan, Dennis P. 60:algebraic topology 33:topological spaces 366: 365: 193:, then the space 132:are modules over 58:, more precisely 16:(Redirected from 421: 387: 380: 373: 345: 338: 330: 319: 300: 162:is unique up to 100:simply connected 92:rational numbers 21: 429: 428: 424: 423: 422: 420: 419: 418: 404:Homotopy theory 394: 393: 392: 391: 334: 328: 317: 309:Ranicki, Andrew 303: 298: 282: 279: 242: 130:homology groups 80: 45:Dennis Sullivan 31:, well-behaved 23: 22: 15: 12: 11: 5: 427: 425: 417: 416: 411: 406: 396: 395: 390: 389: 382: 375: 367: 364: 363: 346: 332: 331: 326: 301: 296: 278: 275: 274: 273: 268: 263: 258: 253: 251:Local analysis 241: 238: 197:is called the 156: 155: 136: 79: 76: 24: 14: 13: 10: 9: 6: 4: 3: 2: 426: 415: 412: 410: 407: 405: 402: 401: 399: 388: 383: 381: 376: 374: 369: 368: 362: 360: 356: 352: 347: 344: 340: 335: 329: 327:1-4020-3511-X 323: 316: 315: 310: 306: 302: 299: 297:0-691-08206-5 293: 289: 285: 281: 280: 276: 272: 269: 267: 264: 262: 259: 257: 254: 252: 249: 248: 247: 246: 239: 237: 235: 231: 227: 223: 219: 215: 212:The map from 210: 208: 204: 200: 196: 192: 188: 184: 179: 177: 173: 169: 165: 161: 153: 149: 145: 141: 138:The map from 137: 135: 131: 127: 123: 120: 119: 118: 116: 112: 108: 104: 101: 97: 93: 89: 85: 77: 75: 73: 69: 65: 61: 57: 52: 50: 49:Sullivan 2005 46: 42: 38: 34: 30: 19: 359:expanding it 348: 333: 313: 287: 284:Adams, Frank 243: 233: 229: 225: 222:isomorphisms 217: 213: 211: 206: 202: 199:localization 198: 194: 190: 186: 182: 180: 175: 171: 168:localization 167: 159: 157: 151: 147: 143: 139: 133: 125: 121: 114: 110: 106: 95: 83: 81: 71: 67: 63: 53: 36: 26: 189:at a prime 158:This space 78:Definitions 29:mathematics 18:Local space 398:Categories 277:References 117:such that 103:CW complex 94:, and let 224:from the 37:localized 307:(2005), 286:(1978), 240:See also 220:induces 56:topology 311:(ed.), 90:of the 88:subring 82:We let 35:can be 324:  294:  349:This 318:(PDF) 98:be a 86:be a 355:stub 322:ISBN 292:ISBN 216:to 205:at 201:of 181:If 178:. 174:at 170:of 150:to 142:to 124:is 113:to 51:). 27:In 400:: 236:. 209:. 74:. 386:e 379:t 372:v 361:. 234:Y 230:X 226:A 218:Y 214:X 207:p 203:X 195:Y 191:p 187:Z 183:A 176:A 172:X 160:Y 152:A 148:X 144:Y 140:X 134:A 126:A 122:Y 115:Y 111:X 107:Y 96:X 84:A 72:Y 68:X 64:X 20:)

Index

Local space
mathematics
topological spaces
localization of a ring
Dennis Sullivan
Sullivan 2005
topology
algebraic topology
subring
rational numbers
simply connected
CW complex
homology groups
homotopy equivalence
isomorphisms
Category:Localization (mathematics)
Local analysis
Localization of a category
Localization of a module
Localization of a ring
Bousfield localization
Adams, Frank
ISBN
0-691-08206-5
Sullivan, Dennis P.
Ranicki, Andrew
Geometric Topology: Localization, Periodicity and Galois Symmetry: The 1970 MIT Notes
ISBN
1-4020-3511-X
Stub icon

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