Stable Homotopy and Generalised Homology

Description

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. I S.P. Novikov's Work on Operations on Complex Cobordism Introduction Cobordism Groups Homology The Conner-Floyd Chern Classes The Novikov Operations The algebra of all operations Scholium on Novikov's Exposition Complex Manifolds II Quillen's Work on Formal Groups and Complex Cobordism Introduction Formal Groups Examples from Algebraic Topology Reformulation Calculations in E-Homology and Cohomology Lazard's Universal Ring More calculations in E-Homology The Structure of Lazard's Universal Ring L Quillen's Theorem Corollaries Various Formulae in (MU) MU(MU) Behaviour of the Bott map K(K) The Hattori-Stong theorem Quillen's Idempotent Cohomology Operations The Brown-Peterson spectrum KO(KO) (Added May 1970) III Stable Homotopy and Generalized Homology Introduction Spectra Elementary properties of the category of CW-spectra Smash products Spanier-Whitehead Duality Homology and Cohomology The Atiyah-Hirzebruch Spectral Sequence The Inverse Limit and its Derived Functors Products Duality in Manifolds Applications in K-Theory The Steenrod Algebra and its Dual A Universal Coefficient Theorem A Category of Fractions The Adams spectral sequence Applications to (bu X); Modules over K[x, y] Structure of *(bubu)