000			02308nam a22002057a 4500
003			OSt
005			20240828162913.0
008			190222b ||||| |||| 00| 0 eng d
020			_a9780821829677
040			_cEducation Supplies _aICTS-TIFR
050			_aQA3
100			_aRavenel, Douglas C.
245			_aComplex cobordism and stable homotopy groups of spheres _b: 2 nd ed.
250			_a2 ed.
260			_aUSA: _bAMS, _c[c2004]
300			_a395 p
505			_aChapter 1. An introduction to the homotopy groups of spheres Chapter 2. Setting up the Adams spectral sequence Chapter 3. The classical Adams spectral sequence Chapter 4. BP-theory and the Adams-Novikov spectral sequence Chapter 5. The chromatic spectral sequence Chapter 6. Morava stabilizer algebras Chapter 7. Computing stable homotopy groups with the Adams-Novikov spectral sequence
520			_aSince the publication of its first edition, this book has served as one of the few available on the classical Adams spectral sequence, and is the best account on the Adams-Novikov spectral sequence. This new edition has been updated in many places, especially the final chapter, which has been completely rewritten with an eye toward future research in the field. It remains the definitive reference on the stable homotopy groups of spheres. The first three chapters introduce the homotopy groups of spheres and take the reader from the classical results in the field though the computational aspects of the classical Adams spectral sequence and its modifications, which are the main tools topologists have to investigate the homotopy groups of spheres. Nowadays, the most efficient tools are the Brown-Peterson theory, the Adams-Novikov spectral sequence, and the chromatic spectral sequence, a device for analyzing the global structure of the stable homotopy groups of spheres and relating them to the cohomology of the Morava stabilizer groups. These topics are described in detail in Chapters 4 to 6. The revamped Chapter 7 is the computational payoff of the book, yielding a lot of information about the stable homotopy group of spheres. Appendices follow, giving self-contained accounts of the theory of formal group laws and the homological algebra associated with Hopf algebras and Hopf algebroids.
942			_2lcc _cBK
999			_c2365 _d2365