828 Index G-maps, 216 G-space, 216 Ganea condition, 257, 713, 741 Ganea construction, 254, 395, 444, 665, 666 Ganea’s conjecture, 257 GEM, 451 general position, 295 generalized CW complex, 244 generating complex, 599, 690 generating function, 575 generator, 294 Hn(Sn Z), 502 generic, 734 geometric realization, 297, 342 graded, 795 R-algebra, 796 R-module, 795 algebra, 796 divided polynomial algebra, 796 exterior algebra, 796 module, 796 polynomial algebra, 796 tensor algebra, 796 graded R-algebra, 475 graded abelian group, 460 graded commutative, 419, 796 algebra, 796 algebra, free, 797 graded commutativity, 428 graded module suspension, 795 graded Serre class, 716 graded twist map, 796 Gram-Schmidt, 332 graph, 133, 216 Grassmannian, 231 group as a category, 6 group object, 21 commutative, 25 Gysin sequence, 675, 682 h∗-equivalence, 734 h∗-local, 734 H-map, 226 fiber, 227 H-space, 226 characterization, 226 product, 227 projective space, 553 retract, 226 strict unit, 226 Hahn-Mazurkowicz, 75 half-smash product, 64 with suspension, 140 halo, 319 Hawaiian earring, 371 HELP, 282 Hilton-Milnor theorem, 390 holonomy, 205 homogeneous, 460 homogeneous coordinates, 52 homology, 384, 544 algebraic, 544, 798 cellular structure, 504 connectivity, 502 Moore space, 567 spheres, 502 unitary group, 598 homology decompositions, 569 homology group, 544 homology module, 798 homology suspension, 577, 578 homology theory, 500 homomorphism, 24, 226, 454 of modules, 789 homotopic, 70, 72, 74, 267 homotopy, 70, 72, 92, 95, 145, 267 cell-by-cell construction, 56 constant, 74 free, 70, 72 Moore, 376 of diagram morphisms, 145 of homotopies, 74 of paths, 72 pointed, 70 reverse, 74 straight-line, 75 under A, 95 unpointed, 70 homotopy category, 261, 268 pointed, 80 unpointed, 80 homotopy classes, 70 homotopy cocartesian cube, 405 homotopy cocartesian square, 405 homotopy colimit, 151, 176, 271 pointed vs. unpointed, 214 Quillen-Serre, 341 standard, 155 homotopy commutative, 81 homotopy equivalence, 92, 96 of diagrams, 144, 145 pointwise, 93, 144 homotopy equivalent, 81, 267 maps, 93 Homotopy Extension Lifting Property, 282 homotopy extension property, 100 homotopy fiber, 131 homotopy fixed point, 218 homotopy functor, 71 homotopy groups, 87 exact sequence of cofibration, 409 finite, 570

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