Complex Cobordism And Stable Homotopy Groups Of Spheres, Volume 121 (pure And Applied Mathematics)
1986 / English / PDF
15.8 MB Download
Since 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. The book is
intended for anyone wishing to study computational stable homotopy
theory. It is accessible to graduate students with a knowledge of
algebraic topology and recommended to anyone wishing to venture
into the frontiers of the subject.
Since 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. The book is
intended for anyone wishing to study computational stable homotopy
theory. It is accessible to graduate students with a knowledge of
algebraic topology and recommended to anyone wishing to venture
into the frontiers of the subject.