 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
|
|
|
Isomorphism Conjectures in K- and L-Theory
未刊 ご予約承ります。
Title: Isomorphism Conjectures in K- and L-Theory Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, Vol. 78 Author: Luck, Wolfgang; Winges, Christoph Publisher: Springer ISBN: 9783031989759 Cover: HARDCOVER Date: 2025年10月 DESCRIPTION This monograph is devoted to the Isomorphism Conjectures formulated by Baum and Connes, and by Farrell and Jones. These conjectures are central to the study of the topological K-theory of reduced group C*-algebras and the algebraic K- and L-theory of group rings. They have far-reaching applications in algebra, geometry, group theory, operator theory, and topology. The book provides a detailed account of the development of these conjectures, their current status, methods of proof, and their wide-ranging implications. These conjectures are not only powerful tools for concrete computations but also play a crucial role in proving other major conjectures. Among these are the Borel Conjecture on the topological rigidity of aspherical closed manifolds, the (stable) Gromov?Lawson?Rosenberg Conjecture on the existence of Riemannian metrics with positive scalar curvature on closed Spin-manifolds, Kaplansky’s Idempotent Conjecture and the related Kadison Conjecture, the Novikov Conjecture on the homotopy invariance of higher signatures, and conjectures concerning the vanishing of the reduced projective class group and the Whitehead group of torsionfree groups. TABLE OF CONTENTS 1 Introduction Part I: Introduction to K- and L-theory 2 The Projective Class Group 3 The Whitehead Group 4 Negative Algebraic K-Theory 5 The Second Algebraic K-Group. 6 Higher Algebraic K-Theory 7 Algebraic K-Theory of Spaces 8 Algebraic K-Theory of Higher Categories 9 Algebraic L-Theory.- 10 Topological K-Theory Part II: The Isomorphism Conjectures 11 Classifying Spaces for Families. 12 Equivariant Homology Theories 13 The Farrell–Jones Conjecture 14 The Baum–Connes Conjecture 15 The (Fibered) Meta- and Other Isomorphism Conjectures 16 Status 17 Guide for Computations 18 Assembly maps.- Part III: Methods of Proofs 19 Motivation, Summary, and History of the Proofs of the Farrell–Jones Conjecture 20 Conditions on a Group Implying the Farrell–Jones Conjecture 21 Controlled Topology Methods 22 Coverings and Flow Spaces 23 Transfer. 24 Higher Categories as Coefficients 25 Analytic Methods 26 Solutions to the Exercises
|
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
