Index 833 structure, 296 simplicial map, 343 simplicial object, 346 simplicial set, 345 simplicial structure, 342 simply-connected, 88, 279, 739 singular chain complex, 551 singular extension, 494, 501 singular simplex, 342 singular simplical set, 346 skeleta, 47 n-equivalence, 358 naturality, 354 skeleton, 47, 572 small diagrams, 30 small object argument, 165 smash product, 61 Eilenberg-Mac Lane spaces, 429 bilinear, 427 contractible, 581 homotopy groups, 427 of CW complexes, 62 smash product pairing, 427 southern hemisphere, 46 space, 54 pointed, 60, 62 spaces over, 94 spaces under, 94 spanning tree, 133 special orthogonal group, 231 special unitary group, 231, 598 spectra, 580 spectral sequence, 645, 647 convergence, 657 first quadrant, 660 free monogenic, 703 homomorphism, 651 of algebras, 653 spectrum, 580 sphere, 45 abelian cogroup in T∗, 86 as pushout, 46 cellular decompositions, 49 homotopy groups, 383 infinite-dimensional, 52 sphere bundle, 677 spherical fibrations, 675 spherically resolvable, 761 split, 223, 795 split exact sequence, 517, 795 stabilizes, 505 stable cohomology operation, 518 additive, 519 stable homotopy groups, 389 homology theory, 505 stable homotopy sets exact sequence, 410 stable operation recognition, 518 stable phenomena, 389 stable range, 389 stably equivalent, 696 standard filtration, 608, 609 of a smash product, 609 standard form, 292 Steenrod algebra, 519, 777 basis, 537 Hopf algebra, 584 Steenrod operations, 527 main properties, 533 Steenrod reduced powers, 525 Steenrod square, 527 indecomposable, 536 stereographic projection, 46 Stiefel manifold, 232, 599 strictly commutative, 82 Strøm model structure, 264 strong deformation retract, 76, 104 strong homotopy pullback square, 189, 307 strong homotopy pushout square, 186 recognition, 186 strong resolving classes, 759, 760 strongly closed classes, 759, 760 strongly cocartesian, 196 strongly homotopy cocartesian, 406 structure, 296, 385 simplicial complex, 296 structure group, 334 subcomplex, 47, 297 subquotient, 606 subsimplex, 296, 342 successor ordinal, 809 Sullivan algebra, 739 Sullivan conjecture, 785 sum, 17, 18, 38 infinite, 807 support, 309 surface, 572 suspension, 46, 66, 84, 461, 487, 738, 796 as natural transformation, 379 cogroup object in T∗, 86 connectivity, 383 fiber, 453 functor, 66 graded module, 795 homotopy pushout, 184 of a sphere, 67 reduced, 66 unreduced, 46 suspension map, 379 symmetric polynomial, 535, 683, 806 symmetric product, 576 Eilenberg-Mac Lane space, 451 homology, 576

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