Bordism, stable homotopy and Adams spectral sequences
type: Item
instance of: scholarly article
title: Bordism, stable homotopy and Adams spectral sequences
zbMATH Open document ID: 0861.55001
published in: Fields Institute Monographs
publication date: 1996-10-28T00:00:00Z
review text: 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.
reviewed by: Katsumi Shimomura
Mathematics Subject Classification ID: 55-02
Mathematics Subject Classification ID: 55P42
Mathematics Subject Classification ID: 55N20
Mathematics Subject Classification ID: 55N22
Mathematics Subject Classification ID: 55Q45
Mathematics Subject Classification ID: 55R40
Mathematics Subject Classification ID: 55T10
Mathematics Subject Classification ID: 55T15
Mathematics Subject Classification ID: 55T25
zbMATH DE Number: 939293
zbMATH Keywords: stable homotopy theory
zbMATH Keywords: nilpotence
zbMATH Keywords: periodicity
zbMATH Keywords: cobordism
zbMATH Keywords: characteristic classes
zbMATH Keywords: spectra
zbMATH Keywords: Brown-Peterson spectrum
zbMATH Keywords: spectral sequences
zbMATH Keywords: Adams spectral sequence
zbMATH Keywords: Adams-Novikov spectral sequence
zbMATH Keywords: stable homotopy groups of spheres
zbMATH Keywords: homology
zbMATH Keywords: cohomology
zbMATH Keywords: classifying spaces
author: Stanley O. Kochman
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 939293