Isomorphism Conjectures in K- and L-Theory
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...
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| Yhteisötekijä: | |
| Aineistotyyppi: | Elektroninen E-kirja |
| Kieli: | englanti |
| Julkaistu: |
Cham :
Springer Nature Switzerland : Imprint: Springer,
2025.
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| Painos: | 1st ed. 2025. |
| Sarja: | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,
78 |
| Aiheet: | |
| Linkit: | https://doi.org/10.1007/978-3-031-98976-6 |
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Sisällysluettelo:
- 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.