238:— expand into a "nexus" to cover the various topological and algebraic "elementary" cases; tie the strings together with showing the derived category formulation for sheaves that generalises all of the special cases
551:
Second priority for now. Branches out very fast towards all other parts of AG and category theory (toposes, gerbes, Tannakian formalism, intersection theory,...)
198:—review and improve; link to sheaf cohomology in general and provide pointers to algebraic de Rham cohomology, the Hodge - de Rham spectral sequence and all that;
342:
show how
Eilenberg-Steenrod fits nicely into a (derived-category) sheaf cohomology (need cohomology with supports / local cohomology)
269:
221:
593:
583:
338:— serious expansion into the nexus of "geometrical" (co)homology theories; most specialist topics into sub-articles;
355:
527:
512:
125:— to combine with Cohomology; an overview of (co-)homology in all places it is used in, not only algebraic topology
134:— to combine with Homology; an overview of (co-)homology in all places it is used in, not only algebraic topology
517:
507:
532:
375:
370:
211:
618:
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522:
118:
38:
365:
578:
360:
274:
613:
563:
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261:
181:
171:
86:
The bold face word after title gives planned WP 1.0 importance. Plans for the article follow that.
628:
487:
191:
90:
56:
395:
231:
62:
462:
432:
201:
161:
151:
573:
439:
417:
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331:
294:
77:— add explanation of group structure wrt Abel-Jacobi map (as per own comments on Talk page)
603:
588:
477:
427:
422:
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345:
137:
34:
Commented articles that can and should be improved irrespective of larger reorganisation.
453:
Personally less expertise in the more advanced areas (stable and rational homotopy,...).
558:
537:
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74:
50:
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148:
cohomology theories. Rename accordingly. Treat
Eilenberg-Steenrod axioms briefly.
502:
400:
304:
251:
241:
17:
314:
128:
59:— redo de Rham's theorem and especially its proof (see own Talk page comment)
608:
482:
248:— expand to cover cup product in its various incarnations; see Künneth above
467:
68:
41:— essentially a rewrite: explain in terms of relative de Rham cohomology
158:— change current redirect to point to the (new) Homology theory (above)
623:
44:
553:
To handle together with the larger AG theme once its time comes.
101:— The main article to organise the whole area. Should give a
47:— essentially a rewrite — now in progress (albeit slowly...)
168:— combine with Singular cohomology; review and improve
71:— contribute along the lines of the talk page comments
178:— combine with Singular homology; review and improve
144:- Develop into an overview of topological homology
53:— rewiew, correct and expan (definition fixed)
8:
113:"Classical" homology / cohomology theories
105:overview with limited technical detail.
82:Algebraic topology and cohomology theme
326:Sheaf cohomology and related theories
7:
65:— add derived category sheaf version
24:
547:Algebraic and analytical geometry
208:— review and improve as necessary
218:—review and improve as necessary
356:compactly-supported cohomology
270:Talk:Poincaré duality/Comments
30:Individual articles to work on
1:
222:universal coefficient theorem
594:variation of Hodge structure
584:algebraic de Rham cohomology
645:
528:spectrum (homotopy theory)
513:homotopy groups of spheres
518:rational homotopy theory
533:Eilenberg-MacLane space
508:exact homotopy sequence
376:Leray spectral sequence
371:Intersection cohomology
212:Mayer-Vietoris sequence
619:crystalline cohomology
599:Gauss-Manin connection
523:stable homotopy theory
119:Homology (mathematics)
39:Gauss-Manin connection
366:Intersection homology
579:Dolbeault cohomology
361:Borel-Moore homology
275:characteristic class
564:coherent cohomology
413:homological algebra
407:Homological algebra
258:— review and expand
228:—review and improve
188:—review and improve
182:Simplicial homology
172:Singular cohomology
629:motivic cohomology
488:suspension functor
192:de Rham cohomology
91:Algebraic topology
57:de Rham cohomology
463:fundamental group
433:spectral sequence
202:cellular homology
162:Singular homology
152:Cohomology theory
636:
614:Ă©tale cohomology
574:coherent duality
449:Homotopy-related
440:derived category
418:abelian category
351:local cohomology
332:sheaf cohomology
295:Pontryagin class
262:Poincaré duality
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604:vanishing cycle
589:hodge structure
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478:homotopy theory
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445:
428:hypercohomology
423:derived functor
409:
396:KĂĽnneth formula
386:Verdier duality
346:Cech cohomology
328:
232:KĂĽnneth formula
138:Homology theory
115:
109:
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63:KĂĽnneth formula
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559:coherent sheaf
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538:model category
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473:homotopy group
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458:covering space
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391:six operations
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75:Elliptic curve
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51:coherent sheaf
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569:Serre duality
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498:wedge product
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493:smash product
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285:Whitney class
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103:comprehensive
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381:Local system
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503:cofibration
401:cup product
305:Chern class
252:cap product
242:cup product
18:User:Stca74
315:Thom class
129:Cohomology
609:monodromy
483:fibration
317:: :
468:homotopy
69:Integral
624:motive
268:— see
340:goal:
99:VITAL
45:Gerbe
16:<
336:HIGH
279:HIGH
266:HIGH
156:HIGH
142:HIGH
97:and
321:TBD
319:MID
311:TBD
309:MID
301:TBD
299:MID
291:TBD
289:MID
281:TBD
256:MID
246:MID
236:MID
226:MID
216:MID
206:MID
196:MID
186:MID
176:MID
166:MID
146:and
132:TOP
123:TOP
95:TOP
334::
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93::
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