Bordism, stable homotopy and Adams spectral sequences
As the author writes the aim of this book is to prepare students with a knowledge of elementary algebraic topology, to study recent developments in stable homotopy theory, such as the nilpotence and periodicity theorems. Actually, this book is designed to understand stable homotopy theory from the viewpoint of the hard homotopy theory, through calculation. In order to understand the recent developments, it introduces all necessary conceptions like cobordism, characteristic classes, spectra, the Brown-Peterson spectrum, etc., and tools such as spectral sequences including the Adams spectral sequence and the Adams-Novikov spectral sequence. Then it presents how to use these tools by the computation of the 2-primary part of stable homotopy groups of spheres up to dimension 30 as well as the determination of the homology and the cohomology of classifying spaces. Besides, each chapter ends with ``Further Reading'' to help interested readers to find more details on the topics of that chapter. By these, students would have a good grip of stable homotopy theory.
scientific article; zbMATH DE number 939293