Stable Homotopy and Generalised Homology
J. Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in 1967, 1970, and 1971, the well-written notes of which are published in this classic in algebraic topology. The three series focused on Novikov's work on operations in complex cobordism, Quillen's work on formal groups and complex cobordism, and stable homotopy and generalized homology. Adams's exposition of the first two topics played a vital role in setting the stage for modern work on periodicity phenomena in stable homotopy theory. His exposition on the third topic occupies the bulk of the book and gives his definitive treatment of the Adams spectral sequence along with many detailed examples and calculations in KU-theory that help give a feel for the subject.
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abelian group assume base-point bundle canonical cells Chern classes cobordism coefficients cofibering cofinal cohomology operation cohomology theories commutative diagram comodule complex consider construct coproduct COROLLARY CW-complex CW-spectrum define degree diagram is commutative dimension E-complete E-equivalence element EP(X exact sequence example filtration finite spectrum finite-dimensional following commutative diagram following diagram formal group formal power-series formal product formula free module function functor give homology and cohomology homomorphism homotopy class homotopy equivalence homotopy groups Hopf algebra integer inverse isomorphism K-theory LEMMA manifold map f module monomorphism morphism Novikov obtain ordinary homology product map properties PROPOSITION prove quotient result ring ring-spectrum satisfies Similarly smash products space spectral sequence stable homotopy Steenrod Steenrod algebra subcomplex subspectrum Suppose given Tel(X theorem topology trivial universal coefficient theorem Whitney sum zero
Page 373 - Homotopy groups of joins and unions, Trans. Amer. Math. Soc. 83 (1956), 55-69.