Induction Theorems and Isomorphism Conjectures for K- and L-Theory

DOI10.1515/FORUM.2007.016zbMath1141.19001arXivmath/0404486WikidataQ122983383 ScholiaQ122983383MaRDI QIDQ5443997

Wolfgang Lück, Arthur C. Bartels

Publication date: 22 February 2008

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0404486

zbMATH Keywords

\(K\)-theoryinductiongroup ring\(L\)-theory

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Computations of higher (K)-theory of rings (19D50) (K_0) of group rings and orders (19A31) (K_1) of group rings and orders (19B28) (L)-theory of group rings (19G24)

Related Items

Modular Symbols and the Topological Nonrigidity of Arithmetic Manifolds ⋮ On the Farrell-Jones conjecture for algebraic \(K\)-theory of spaces: the Farrell-Hsiang method ⋮ Algebraic K-theory of group rings and the cyclotomic trace map ⋮ On the transfer reducibility of certain Farrell-Hsiang groups ⋮ On products in algebraic \(K\)-theory of crossed Hopf algebras ⋮ The K and L Theoretic Farrell-Jones Isomorphism Conjecture for Braid Groups ⋮ Algebraic \(K\)-theory over virtually abelian groups ⋮ The Farrell-Jones Conjecture for cocompact lattices in virtually connected Lie groups ⋮ Unnamed Item ⋮ \(K\)- and \(L\)-theory of graph products of groups ⋮ On algebraic \(K\)-functors of crossed group rings and its applications

Cites Work

• Induced representations and projective modules
• Families of subgroups and completion
• Induction and structure theorems for orthogonal representations of finite groups
• Rational L-groups of Bieberbach groups
• Spaces over a category and assembly maps in isomorphism conjectures in \(K\)- and \(L\)-theory
• Higher \(K\)-theory of group-rings of virtually infinite cyclic groups
• Identifying assembly maps in \(K\)- and \(L\)-theory
• Equivariant \(K\)-homology and restriction to finite cyclic subgroups
• The lower algebraic \(K\)-theory of virtually infinite cyclic groups
• The Grothendieck ring of a finite group
• Chern characters for proper equivariant homology theories and applications to K- and L-theory
• The Wall Finiteness Obstruction for a Fibration
• Lower k-theory of finite groups
• Isomorphism Conjectures in Algebraic K-Theory
• Unitary nilpotent groups and Hermitian $K$-theory. I
• A Caveat on the Isomorphism Conjecture in L-theory