Knowledge (XXG)

L² cohomology

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606: 549: 590: 583: 647: 394:. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics . Vol. 44. Berlin: Springer-Verlag. 681: 576: 399: 351: 123: 206: 676: 671: 194: 666: 84:
L cohomology, which grew in part out of L d-bar estimates from the 1960s, was studied cohomologically, independently by
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Cheeger, J.; Goresky, M.; MacPherson, R. "L cohomology and intersection homology for singular algebraic varieties".
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Zucker, Steven (1979). "Hodge theory with degenerating coefficients: L-cohomology in the Poincaré metric".
240:. Proc. Sympos. Pure Math. Vol. 36. Providence, R.I.: American Mathematical Society. pp. 91–146. 633: 362: 96:; indeed, the results in the preceding cited works can be expressed in terms of intersection cohomology. 556: 471: 419: 511: 266: 66: 153: 148: 527: 488: 436: 74: 55: 395: 347: 302: 119: 104: 62: 59: 51: 36: 617: 560: 519: 480: 428: 383: 357: 292: 274: 215: 127: 448: 375: 323: 288: 245: 229: 444: 371: 319: 284: 241: 225: 40: 515: 270: 339: 167: 143: 297: 254: 660: 531: 85: 330: 201: 173: 89: 334: 17: 500:
Zucker, Steven (1982). "L-cohomology of warped products and arithmetic groups".
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Cheeger, Jeff (1980). "On the Hodge theory of Riemannian pseudomanifolds".
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Zucker, Steven (1978). "Théorie de Hodge à coefficients dégénérescents".
44: 170:(1976). "Elliptic operators, discrete groups and von Neumann algebras". 548: 523: 492: 440: 484: 432: 318:. Annals of Mathematics Studies. Vol. 102. pp. 303–340. 178:. Paris: Soc. Math. France. pp. 43–72. Astérisque, No. 32–33. 255:"On the spectral geometry of spaces with cone-like singularities" 65:. The notion of square-integrability makes sense because the 204:(1983), "Spectral geometry of singular Riemannian spaces", 621: 564: 360:(1988). "L-cohomology of locally symmetric varieties". 388:
L-invariants: theory and applications to geometry and
126:(Zucker 1982). This was proved in different ways by 344:An Introduction to Intersection Homology Theory, 172:Colloque "Analyse et Topologie" en l'Honneur de 641: 584: 8: 648: 634: 591: 577: 296: 278: 219: 335:L cohomology is intersection cohomology 417:-cohomology of arithmetic varieties". 7: 602: 600: 545: 543: 54:. It is defined in the same way as 620:. You can help Knowledge (XXG) by 563:. You can help Knowledge (XXG) by 25: 92:(1979). It is closely related to 604: 547: 316:Seminar on Differential Geometry 238:Geometry of the Laplace operator 207:Journal of Differential Geometry 130:(1988) and by Leslie Saper and 185:"Baily–Borel compactification" 1: 259:Proc. Natl. Acad. Sci. U.S.A 124:Baily–Borel compactification 77:on differential forms and a 682:Differential geometry stubs 190:Encyclopedia of Mathematics 99:Another such result is the 703: 599: 542: 183:Gordon, B. Brent (2001) , 103:, which states that for a 108:locally symmetric variety 503:Inventiones Mathematicae 116:intersection cohomology 94:intersection cohomology 559:-related article is a 458:Compt. Rend. Acad. Sci 363:Compositio Mathematica 280:10.1073/pnas.76.5.2103 253:Cheeger, Jeff (1979). 221:10.4310/jdg/1214438175 677:Differential topology 672:Differential geometry 557:differential geometry 472:Annals of Mathematics 420:Annals of Mathematics 58:except that one uses 110:the L cohomology is 667:Cohomology theories 516:1982InMat..70..169Z 271:1979PNAS...76.2103C 154:Riemannian manifold 149:Dirichlet principle 524:10.1007/BF01390727 168:Atiyah, Michael F. 63:differential forms 56:de Rham cohomology 629: 628: 572: 571: 423:. Second Series. 358:Looijenga, Eduard 342:, Jonathan Woolf 120:middle perversity 101:Zucker conjecture 60:square-integrable 52:Riemannian metric 37:cohomology theory 18:Zucker conjecture 16:(Redirected from 694: 650: 643: 636: 614:topology-related 608: 601: 593: 586: 579: 551: 544: 535: 496: 465: 452: 405: 379: 327: 310: 300: 282: 265:(5): 2103–2106. 249: 232: 223: 197: 179: 128:Eduard Looijenga 73:gives rise to a 21: 702: 701: 697: 696: 695: 693: 692: 691: 657: 656: 655: 654: 598: 597: 540: 538: 499: 485:10.2307/1971221 468: 455: 433:10.2307/1971500 416: 409:Saper, Leslie; 408: 402: 382: 356: 313: 252: 235: 200: 182: 166: 162: 140: 23: 22: 15: 12: 11: 5: 700: 698: 690: 689: 687:Topology stubs 684: 679: 674: 669: 659: 658: 653: 652: 645: 638: 630: 627: 626: 609: 596: 595: 588: 581: 573: 570: 569: 552: 537: 536: 510:(2): 169–218. 497: 479:(3): 415–476. 466: 453: 414: 406: 400: 384:Lück, Wolfgang 380: 354: 340:Frances Kirwan 337: 328: 311: 250: 233: 214:(4): 575–657, 198: 180: 163: 161: 158: 157: 156: 151: 146: 144:Dirichlet form 139: 136: 24: 14: 13: 10: 9: 6: 4: 3: 2: 699: 688: 685: 683: 680: 678: 675: 673: 670: 668: 665: 664: 662: 651: 646: 644: 639: 637: 632: 631: 625: 623: 619: 616:article is a 615: 610: 607: 603: 594: 589: 587: 582: 580: 575: 574: 568: 566: 562: 558: 553: 550: 546: 541: 533: 529: 525: 521: 517: 513: 509: 505: 504: 498: 494: 490: 486: 482: 478: 474: 473: 467: 463: 459: 454: 450: 446: 442: 438: 434: 430: 426: 422: 421: 412: 407: 403: 401:3-540-43566-2 397: 393: 389: 385: 381: 377: 373: 369: 365: 364: 359: 355: 353: 352:1-58488-184-4 349: 345: 341: 338: 336: 332: 329: 325: 321: 317: 312: 308: 304: 299: 294: 290: 286: 281: 276: 272: 268: 264: 260: 256: 251: 247: 243: 239: 234: 231: 227: 222: 217: 213: 209: 208: 203: 202:Cheeger, Jeff 199: 196: 192: 191: 186: 181: 177: 176:(Orsay, 1974) 175: 169: 165: 164: 159: 155: 152: 150: 147: 145: 142: 141: 137: 135: 133: 129: 125: 121: 117: 113: 109: 106: 102: 97: 95: 91: 87: 86:Steven Zucker 82: 80: 76: 72: 68: 64: 61: 57: 53: 49: 46: 42: 38: 34: 30: 19: 622:expanding it 611: 565:expanding it 554: 539: 507: 501: 476: 470: 464:: 1137–1140. 461: 457: 424: 418: 391: 387: 367: 361: 346:, chapter 6 343: 331:Mark Goresky 315: 262: 258: 237: 211: 205: 188: 174:Henri Cartan 171: 100: 98: 90:Jeff Cheeger 83: 70: 47: 43:non-compact 33:L cohomology 32: 26: 427:(1): 1–69. 411:Stern, Mark 370:(1): 3–20. 88:(1978) and 79:volume form 29:mathematics 661:Categories 413:(1990). "L 160:References 132:Mark Stern 118:(with the 112:isomorphic 532:121348276 195:EMS Press 122:) of its 105:Hermitian 45:manifolds 386:(2002). 307:16592646 138:See also 134:(1990). 512:Bibcode 493:1971221 449:1059935 441:1971500 392:-theory 376:0949269 324:0645745 289:0530173 267:Bibcode 246:0573430 230:0730920 114:to the 530:  491:  447:  439:  398:  374:  350:  322:  305:  298:383544 295:  287:  244:  228:  67:metric 41:smooth 612:This 555:This 528:S2CID 489:JSTOR 437:JSTOR 50:with 35:is a 618:stub 561:stub 396:ISBN 348:ISBN 303:PMID 75:norm 39:for 520:doi 481:doi 477:109 462:286 429:doi 425:132 293:PMC 275:doi 216:doi 69:on 27:In 663:: 526:. 518:. 508:70 506:. 487:. 475:. 460:. 445:MR 443:. 435:. 372:MR 368:67 366:. 333:, 320:MR 301:. 291:. 285:MR 283:. 273:. 263:76 261:. 257:. 242:MR 226:MR 224:, 212:18 210:, 193:, 187:, 81:. 31:, 649:e 642:t 635:v 624:. 592:e 585:t 578:v 567:. 534:. 522:: 514:: 495:. 483:: 451:. 431:: 415:2 404:. 390:K 378:. 326:. 309:. 277:: 269:: 248:. 218:: 71:M 48:M 20:)

Index

Zucker conjecture
mathematics
cohomology theory
smooth
manifolds
Riemannian metric
de Rham cohomology
square-integrable
differential forms
metric
norm
volume form
Steven Zucker
Jeff Cheeger
intersection cohomology
Hermitian
locally symmetric variety
isomorphic
intersection cohomology
middle perversity
Baily–Borel compactification
Eduard Looijenga
Mark Stern
Dirichlet form
Dirichlet principle
Riemannian manifold
Atiyah, Michael F.
Henri Cartan
"Baily–Borel compactification"
Encyclopedia of Mathematics

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