Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem

Michael A. Hill

ISBN 10: 1108831443 / ISBN 13: 9781108831444

Edité par Cambridge University Press, 2021

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - 'This unique book on modern topology looks well beyond traditional treatises, and explores spaces that may, but need not, be Hausdorff. This is essential for domain theory, the cornerstone of semantics of computer languages, where the Scott topology is almost never Hausdorff. For the first time in a single volume, this book covers basic material on metric and topological spaces, advanced material on complete partial orders, Stone duality, stable compactness, quasi-metric spaces, and much more. An early chapter on metric spaces serves as an invitation to the topic (continuity, limits, compactness, completeness) and forms a complete introductory course by itself'--.

N° de réf. du vendeur 9781108831444

Détails bibliographiques

• Titre: Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem
• Éditeur: Cambridge University Press
• Date de parution: 2021
• Langue: anglais
• ISBN à 10 chiffres: 1108831443
• ISBN à 13 chiffres: 9781108831444
• Reliure: Buch
• État de l'article: Neu
• Dimensions: 250 L x 175 H x 51 P (en millimètres) 250 millimètres de largeur par 175 millimètres de hauteur par 51 millimètres de profondeur
• Poids: 1670 grammes

A propos de ce titre

Synopsis

The long-standing Kervaire invariant problem in homotopy theory arose from geometric and differential topology in the 1960s and was quickly recognised as one of the most important problems in the field. In 2009 the authors of this book announced a solution to the problem, which was published to wide acclaim in a landmark Annals of Mathematics paper. The proof is long and involved, using many sophisticated tools of modern (equivariant) stable homotopy theory that are unfamiliar to non-experts. This book presents the proof together with a full development of all the background material to make it accessible to a graduate student with an elementary algebraic topology knowledge. There are explicit examples of constructions used in solving the problem. Also featuring a motivating history of the problem and numerous conceptual and expository improvements on the proof, this is the definitive account of the resolution of the Kervaire invariant problem.

À propos des auteurs

Michael A. Hill is Professor at the University of California, Los Angeles. He is the author of several papers on algebraic topology and is an editor for journals including Mathematische Zeitschrift and Transactions of the American Mathematical Society.

Michael J. Hopkins is Professor at Harvard University. His research concentrates on algebraic topology. In 2001, he was awarded the Oswald Veblen Prize in Geometry from the AMS for his work in homotopy theory, followed by the NAS Award in Mathematics in 2012 and the Nemmers Prize in Mathematics in 2014.

Douglas C. Ravenel is the Fayerweather Professor of Mathematics at the University of Rochester. He is the author of two influential previous books in homotopy theory and roughly 75 journal articles on stable homotopy theory and algebraic topology.