Index 825 cohomology, 460 BZ/p, 520 algebraic, 544 coeﬃcients, 460 exact sequence of fibration, 583 James construction, 480 of a product, 488 of Moore space, 470 projective space, 470 reduced, 467 telescope, 465 unitary group, 597 unreduced, 467 with local coeﬃcients, 625 cohomology algebra projective space, 480 cohomology class, 460 cohomology group, 544 cohomology operation, 516 Moore space, 567 cohomology theory, 459, 461 extraordinary, 462 multiplictative, 586 ordinary, 462 colimit, 15, 34 3 × 3 diagram, 41 I × J diagram, 42 commute with adjoint, 35 naturality, 34 pushout, 37 collapse, 654 commutative, 4, 25, 227, 475, 792 on the nose, 82 graded, 419, 796 homotopy, 81 strictly, 82 commutative differential graded algebra, 739 commutativity graded, 418 commutator, 388 commutator subgroup, 388 compact, 97 compact subspace of CW complex, 50 compact-open topology, 54 compactly generated, 55 compactness and CW complexes, 49 comparison cofiber to suspension of fiber, 397 cofiber to base, 395 homotopy pullback to homotopy pushout, 394 homotopy pushout to homotopy pullback, 398 comparison map, 51, 394, 397, 398, 463 compatible, 136, 137 complement, 231 complete, 262 completion, 735 component, 795 compressible, 635 comultiplication, 804 concatenate, 374 concatenation, 74 infinite, 277 of homotopies, 73 of paths, 72 rigid, 374 concentrated, 462, 795 cone, 67 reduced, 67 cone decomposition, 237 cellular, 470 cone filtration, 608, 613 cone length A-cone length, 238 Lusternik-Schnirelmann category, 251 of a map, 238 of a space, 239 connected, 797 connected cover, 362 connected sum, 572 connective, 737 connectivity, 279 cohomology, 464 homology, 502 mod Q, 443 mod C, 716 of a space, 279 of half-smash product, 358 of join, 358 of product, 358 of smash product, 358 of smash product of maps, 359 of suspension, 358, 383 constant diagram, 159 constant homotopy, 74 continuity of map from a CW complex, 49 contractible, 82 smash product, 581 contraficients, 427 contravariant functor, 9 converges, 654 converting to fibration, 111, 113 convex, 75 convex combination, 75 coordinate map, 421, 807 coproduct, 17, 38 covariant functor, 8 covering, 326

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