Description
Book SynopsisDescribes some major advances made in algebraic topology, centering on the nilpotence and periodicity theorems. This book begins with some elementary concepts of homotopy theory that are needed to state the problem. The latter portion provides specialists with a coherent and rigorous account of the proofs.
Trade Review"Familiarity with the material of this book is essential for any a serious homotopy theorist... [The author's] important role in the developments will ensure that [this book] will remain an important source for some time."--Bulletin of the London Mathematical Society
Table of Contents*Frontmatter, pg. i*Contents, pg. vii*Preface, pg. xi*Introduction, pg. xiii*Chapter 1. The main theorems, pg. 1*Chapter 2. Homotopy groups and the chromatic filtration, pg. 11*Chapter 3. MU-theory and formal group laws, pg. 25*Chapter 4. Morava's orbit picture and Morava stabilizer groups, pg. 37*Chapter 5. The thick subcategory theorem, pg. 45*Chapter 6. The periodicity theorem, pg. 53*Chapter 7. Bousfield localization and equivalence, pg. 69*Chapter 8. The proofs of the localization, smash product and chromatic convergence theorems, pg. 81*Chapter 9. The proof of the nilpotence theorem, pg. 99*Appendix A. Some tools from homotopy theory, pg. 119*Appendix B. Complex bordism and BP-theory, pg. 145*Appendix C. Some idempotents associated with the symmetric group, pg. 183*Bibliography, pg. 195*Index, pg. 205
