Index

acyclic, 140

algebraic /f-theory, 103-126

of finitely free modules, 114

of spaces, 125-126

Quillen, 114

approximation theorem. 107

Atiyah-Hirzebruch spectral sequence, 80

Atiyah-Segal completion theorem, 166

Baas-Sullivan theory, 91

bar construction, 88, 136, 162, 172, 173,

186-187, 209-214

bar construction spectral sequence, 89

bimodule, 59-61, 65-66, 68, 128, 130

Bott element, 166

Bousfield localization, 155-166

Brown's representability theorem, 58, 75,

76

Brown-Peterson spectrum, 101

category with w-cofibrations, 103

cell algebra, 62

and Bousfield localization, 160, 166

see also g-cofibrant algebra

cell and CW L-spectra, 18, 22

cell and CW modules, 33-34, 54-58, 63,

147-149, 184

and extended powers, see extended power

and extension of scalars, 61, 62

and function modules, 67

and smash products, 60, 61, 69

and symmetric powers, see symmetric

power

cell commutative algebra

and Bousfield localization, 160, 166

see also g-cofibrant commutative alge-

bra

cell T-algebra, 143-144, 147

cellular approximation, 57

cellular chain complex, 75, 79

center, 128

central map, 128

change of universe, 14, 232

CHP, see covering homotopy property

cobar construction. 187

cobase change, 152

cocompleteness, of category of

Aoo ring spectra, 47-49

commutative ^-algebras. 47-49

commutative 5-algebras. 47-49

Eoc ring spectra, 47-49

L-spectra, 18

^-algebras, 47-49

/?-modules, 51

5-algebras, 47-49

5-modules, 32

spectra, 10

cocompleteness, topological, 131

coconnective, 73

coend, 179

coequalizer

homotopy, see double mapping cylin-

der

see also homotopy colimit

reflexive, see reflexive coequalizer

split, see split coequalizer

cofiber, 10, 92

cofiber sequence, 10, 75

and function module, 67, 79

and long exact sequences, 15, 23, 72,

73

and smash product, 23, 59

cofibration, 10, 140, 182, 187

Cofibration Hypothesis, 143

compact ^-module, 53, 55, 201

compact spectrum, 53

completeness, of category of

Aoc ring spectra. 40

commutative H-algebras, 40

commutative 5-algebras, 40

Eoc ring spectra, 40

L-spectra, 18

/^-algebras, 40

/^-modules, 51

5-algebras, 40

5-modules, 32

spectra, 10

completeness, topological, 131

completion, see Bousfield localization

complex /^-theory, see A'-theory

connective, 57

connective /C-theory, see A'-theory

cotensor, 131

counital L-spectra, see mirror image

covering homotopy property, 10, 140

see also fibration

cyclic bar construction, 172

cylinder axiom, 107

cylinder construction, 191-195

cylinder functor, 107

cylinder object, 108, 144

degeneracy subspectrum, 182

247