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Isomorphism Conjectures in K- and L-Theory

By Wolfgang Lück

Isomorphism Conjectures in K- and L-Theory Mathematics

Isomorphism Conjectures in K- and L-Theory

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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.
Product details
Number of Pages:
896
Release Date:
2025-10-02
Publication Date:
2025-10-02
Publisher:
Springer
Languages:
Original: English
ISBN10:
3031989759
ISBN13:
9783031989759
GPSR Manufacturer Reference:
[email protected]
Weight:
1651 g
Height:
160 cm
Width:
241 cm
Thickness:
50 cm
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