Transformation groups and algebraic K-theory / Wolfgang Lück
Type de document : Livre numériqueCollection : Lecture notes in mathematics, 1408Langue : anglais.Éditeur : Berlin : Springer-Verlag, 1989ISBN: 9783540518464.ISSN: 1617-9692.Sujet MSC : 57S17, Manifolds and cell complexes - Topological transformation groups, Finite transformation groups57R67, Manifolds and cell complexes - Differential topology, Surgery obstructions, Wall groups
57Q12, Manifolds and cell complexes - PL-topology, Wall finiteness obstruction for CW-complexes
19Jxx, K-theory - Obstructions from topology
57S15, Manifolds and cell complexes - Topological transformation groups, Compact Lie groups of differentiable transformationsEn-ligne : Springerlink | Zentralblatt | MathSciNet
This book is devoted to the application of algebraic K-theory to problems in transformation groups. The first segment of the book gives the geometric construction of the invariants. The invariants considered include the finiteness obstruction, Whitehead torsion, and the Euler characteristic. The second segment is devoted to the same invariants from an algebraic viewpoint. Here one studies modules over a category and appropriate chain complexes to form algebraic K-groups. The final segment is devoted to further extension of the algebra and application of these ideas to geometry. Here one finds an examination of the homological algebra, introduction of equivariant Reidemeister torsion, Swan homomorphisms, and transfers. (Zentralblatt)
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