Stable Homotopy and Generalised HomologyJ. 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. |
Common terms and phrases
abelian group base-point BU(n bu^X bundle cells Chern classes cobordism coefficients cofibering cofinal cohomology operation cohomology theories commutative diagram comodule complex consider construct COROLLARY corresponding CW-complexes CW-spectrum define degree diagram is commutative dimension E-complete E-equivalence element EP(X exact sequence example filtration finite spectrum following diagram formal group formal power-series formal product formula free module function functor H(MU homology homology and cohomology homomorphism homotopy equivalence homotopy groups Hopf algebra induces inverse isomorphism K-theory LEMMA manifold module monomorphism morphism obtain pair polynomial product map Proof properties PROPOSITION prove result ring ring-spectrum satisfies Similarly smash-product spectral sequence stable homotopy Steenrod Steenrod algebra subspectrum Suppose given Tel(X theorem Thom topology trivial universal coefficient theorem Whitney sum zero α α
References to this book
Rings, Modules, and Algebras in Stable Homotopy Theory Anthony D. Elmendorf No preview available - 1997 |