## Stable homotopy and generalized homology |

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### Contents

Introduction | 1 |

Spectra | 14 |

Elementary Properties of the Category of CWSpectra | 30 |

9 other sections not shown

### Common terms and phrases

abelian group Adams spectral sequence algebra assume axiom boundary buAbu buAX bundle cofibering cofinal cohomology theory commutative diagram comodule completes the proof complex components consider construct corresponding CW-complexes CW-complexes with base-point CW-spectrum define diagram is commutative dimension direct limits duality E-complete E-equivalence Eilenberg-Steenrod element EP(X exact sequence example filtration finite spectrum finite-dimensional following commutative diagram following diagram function functor generalised homology give homology and cohomology homomorphism homotopy class homotopy equivalence homotopy groups induces an isomorphism J. H. C. Whitehead K-theory Kronecker product Lemma 17 manifold map f morphism morphism of degree obvious open pair ordinary homology orientation polynomial properties Proposition prove quotient R-module result ring-spectrum satisfies Similarly smash products spectra spectral sequence stable cells stable homotopy subcomplex Suppose given Susp(X Tel(X trivial universal coefficient theorem zero