834 Index K¨ unneth theorem, 576 symmetric square, 259 symplectic group, 231, 603 system of local coeﬃcients, 625 tab-and-glue, 311 target, 4, 34 target type, 15 telescope cohomology, 465 telescope diagram, 39, 163 tensor algebra, 793 graded, 796 universal property, 793 tensor product, 427, 790 graded, 474 of chain complexes, 799 terminal object, 18 Thom class, 678 Thom Isomorphism Theorem, 678 Thom space, 676, 677 topological space, 54 pointed, 62 total degree, 612, 653 total dimension, 612 total left derived functor, 269 total space, 108 total square, 536 tower, 39, 173 track, 138 transgression, 667, 668 transgressive, 667 transgressive pair, 667 transition functions, 333 tree, 133 tree-like, 159 triad, 402 trivial, 82, 263 trivial bundle, 323 trivial cofibration, 121 trivial fibration, 121, 591 trivial homotopy, 74 trivial morphism, 19 trivialization, 591 truncated polynomial algebras, 793 truncated projective space, 586 twist map, 25, 418, 792 two-cones, 602 type, 743 unique, 53 unital, 475 unitary group, 231 universal bundle existence, 366 universal coeﬃcients decomposition, 634, 700 Universal Coeﬃcients Theorem, 486, 660 universal cover, 328 universal example, 102, 124, 225, 523, 584, 790, 797 universal phantom map, 246 universal problem, 4 universal property, 15 unreduced homology exactness, 500 unreduced homology theory, 500 unstable algebra, 534 unstable conditions, 533, 534 unstable module, 534 unstable relations, 525 vanishes, 360 vector field, 417 versal, 246 vertices, 295 very nice, 780 W-local, 722 Wang cofiber sequence, 594 Wang exact sequence, 594 Wang sequence, 593 cohomology, 594, 595 homology, 595 weak category, 260, 561 weak equivalence, 262, 278 and cohomology, 464 Weak Equivalence Axiom, 461, 463 homology, 501 weak fibration, 306 strong homotopy pullback, 307 weak Hausdorff, 55 weak homotopy equivalence, 278 weak lifting function, 308 weak product, 421 infinite, 376 weakly contractible, 279 weakly equivalent, 263 wedge, 19, 61, 463 Wedge Axiom, 463 homology, 501 well-pointed, 124, 188 cofibration, 126 fibration, 126 mapping space, 126 Whitehead exact sequence, 583 Whitehead product generalized, 225 H-space, 226 Whitney sum, 695 wreath product, 531 X -cellular, 764 X-null, 785

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