Knowledge (XXG)

Robert Riley (mathematician)

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141:, which includes as a particular case a criterion for a knot complement to support a hyperbolic structure. One notable feature of Riley's work is that it relied much on the assistance of a computer. 127: 471:
Brin, Matthew G.; Jones, Gareth A.; Singerman, David (2013). "Commentary on Robert Riley's article "A personal account of the discovery of hyperbolic structures on some knot complements"".
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in 1957; shortly thereafter he dropped out of the graduate program and went on to work in industry, eventually moving to Amsterdam in 1966. In 1968 he took a temporary position at the
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and some others. This was one of the few examples of hyperbolic 3-manifolds that were available at the time, and as such it was one of the motivations which led to William Thurston's
54:. He defended his Ph.D. at this institution in 1980, under the nominal direction of David Singerman. For the next two years he occupied a postdoctoral position in 537: 532: 380: 89: 261: 138: 51: 259:
Riley, Robert (2013). "A personal account of the discovery of hyperbolic structures on some knot complements".
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where William Thurston was employed at the time, before moving on to Binghamton University as a professor.
35: 130: 75: 527: 216: 27: 22:(December 22, 1935–March 4, 2000) was an American mathematician. He is known for his work in 506: 480: 296: 270: 67: 134: 55: 490: 457: 280: 224: 172: 31: 502: 292: 236: 184: 498: 288: 232: 180: 220: 86:, he was interested in morphisms to finite groups. Later on in Southampton, considering 521: 510: 300: 462: 445: 129:-representations sending peripheral elements to parabolics led him to discover the 494: 284: 325: 163: 71: 228: 176: 79: 376: 161:
Riley, Robert (1975a). "Discrete parabolic representations of link groups".
83: 446:"Three dimensional manifolds, Kleinian groups and hyperbolic geometry" 485: 275: 360: 358: 47: 207:
Riley, Robert (1975b). "A quadratic parabolic group".
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Riley earned a bachelor's degree in mathematics from
364: 121: 250: 198: 152: 122:{\displaystyle \mathrm {SL} _{2}(\mathbb {C} )} 450:Bulletin of the American Mathematical Society 8: 333:Notices of the American Mathematical Society 484: 461: 274: 112: 111: 102: 94: 91: 415: 349: 317: 403: 391: 427: 7: 538:20th-century American mathematicians 30:, being one of the inspirations for 98: 95: 14: 326:"Deaths–Robert Freed Riley" 209:Math. Proc. Cambridge Philos. Soc 365:Brin, Jones & Singerman 2013 463:10.1090/S0273-0979-1982-15003-0 116: 108: 82:. Early on, following work of 26:using computational tools and 1: 444:Thurston, William P. (1982). 381:Mathematics Genealogy Project 495:10.1016/j.exmath.2013.01.002 285:10.1016/j.exmath.2013.01.003 554: 74:, where he mostly studied 34:'s later breakthroughs in 473:Expositiones Mathematicae 262:Expositiones Mathematicae 253: 229:10.1017/S0305004100051094 201: 177:10.1112/S0025579300005982 155: 139:geometrisation conjecture 133:on the complement of the 52:University of Southampton 66:Riley's research was in 24:low-dimensional topology 123: 36:3-dimensional topology 16:American mathematician 145:Selected publications 124: 533:American topologists 131:hyperbolic structure 90: 221:1975MPCPS..77..281R 28:hyperbolic geometry 119: 68:geometric topology 309: 308: 245: 244: 193: 192: 135:figure-eight knot 62:Mathematical work 545: 514: 488: 467: 465: 431: 425: 419: 413: 407: 401: 395: 389: 383: 374: 368: 362: 353: 347: 341: 340: 330: 322: 304: 278: 251: 240: 199: 188: 153: 128: 126: 125: 120: 115: 107: 106: 101: 70:, especially in 32:William Thurston 553: 552: 548: 547: 546: 544: 543: 542: 518: 517: 470: 443: 440: 435: 434: 426: 422: 414: 410: 402: 398: 390: 386: 375: 371: 363: 356: 348: 344: 339:(6): 679. 2000. 328: 324: 323: 319: 314: 305: 258: 241: 206: 189: 160: 147: 93: 88: 87: 76:representations 64: 44: 20:Robert F. Riley 17: 12: 11: 5: 551: 549: 541: 540: 535: 530: 520: 519: 516: 515: 468: 456:(3): 357–382. 439: 436: 433: 432: 420: 408: 396: 384: 369: 354: 352:, p. 360. 342: 316: 315: 313: 310: 307: 306: 269:(2): 104–115. 257: 255: 249: 248: 243: 242: 215:(2): 281–288. 205: 203: 197: 196: 191: 190: 171:(2): 141–150. 159: 157: 151: 150: 146: 143: 118: 114: 110: 105: 100: 97: 63: 60: 43: 40: 15: 13: 10: 9: 6: 4: 3: 2: 550: 539: 536: 534: 531: 529: 526: 525: 523: 512: 508: 504: 500: 496: 492: 487: 482: 479:(2): 99–103. 478: 474: 469: 464: 459: 455: 451: 447: 442: 441: 437: 429: 424: 421: 417: 416:Thurston 1982 412: 409: 405: 400: 397: 393: 388: 385: 382: 378: 373: 370: 366: 361: 359: 355: 351: 350:Thurston 1982 346: 343: 338: 334: 327: 321: 318: 311: 302: 298: 294: 290: 286: 282: 277: 272: 268: 264: 263: 256: 252: 247: 246: 238: 234: 230: 226: 222: 218: 214: 210: 204: 200: 195: 194: 186: 182: 178: 174: 170: 166: 165: 158: 154: 149: 148: 144: 142: 140: 136: 132: 103: 85: 81: 77: 73: 69: 61: 59: 57: 53: 49: 41: 39: 37: 33: 29: 25: 21: 476: 472: 453: 449: 423: 411: 399: 387: 377:Robert Riley 372: 345: 336: 332: 320: 266: 260: 212: 208: 168: 162: 65: 45: 19: 18: 528:2000 deaths 404:Riley 1975b 392:Riley 1975a 164:Mathematika 80:knot groups 72:knot theory 522:Categories 438:References 428:Riley 2013 511:119568843 486:1301.4599 301:119319528 276:1301.4601 84:Ralph Fox 503:3057119 379:at the 293:3057120 237:0412416 217:Bibcode 185:0425946 56:Boulder 509:  501:  299:  291:  235:  183:  42:Career 507:S2CID 481:arXiv 329:(PDF) 312:Notes 297:S2CID 271:arXiv 202:R75b. 156:R75a. 254:R13. 491:doi 458:doi 281:doi 225:doi 173:doi 78:of 48:MIT 38:. 524:: 505:. 499:MR 497:. 489:. 477:31 475:. 452:. 448:. 357:^ 337:47 335:. 331:. 295:. 289:MR 287:. 279:. 267:31 265:. 233:MR 231:. 223:. 213:77 211:. 181:MR 179:. 169:22 167:. 513:. 493:: 483:: 466:. 460:: 454:6 430:. 418:. 406:. 394:. 367:. 303:. 283:: 273:: 239:. 227:: 219:: 187:. 175:: 117:) 113:C 109:( 104:2 99:L 96:S

Index

low-dimensional topology
hyperbolic geometry
William Thurston
3-dimensional topology
MIT
University of Southampton
Boulder
geometric topology
knot theory
representations
knot groups
Ralph Fox
hyperbolic structure
figure-eight knot
geometrisation conjecture
Mathematika
doi
10.1112/S0025579300005982
MR
0425946
Bibcode
1975MPCPS..77..281R
doi
10.1017/S0305004100051094
MR
0412416
Expositiones Mathematicae
arXiv
1301.4601
doi

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