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Algebraic K-theory of rings from a topological viewpoint.

Dominique Arlettaz (2000)

Publicacions Matemàtiques

Because of its strong interaction with almost every part of pure mathematics, algebraic K-theory has had a spectacular development since its origin in the late fifties. The objective of this paper is to provide the basic definitions of the algebraic K-theory of rings and an overview of the main classical theorems. Since the algebraic K-groups of a ring R are the homotopy groups of a topological space associated with the general linear group over R, it is obvious that many general results follow...

Cubic structures and ideal class groups

Georgios Pappas (2005)

Annales scientifiques de l'École Normale Supérieure

Divisibility of the Dirac magnetic monopole as a two-vector bundle over the three-sphere.

Ausoni, Christian, Dundas, Bjørn Ian, Rognes, John (2008)

Documenta Mathematica

Equivariant higher $K$ -theory for compact Lie group actions.

Kuku, Aderemi O. (2000)

Beiträge zur Algebra und Geometrie

Filtered topological cyclic homology and relative $K$ -theory of nilpotent ideals.

Brun, Morten (2001)

Algebraic & Geometric Topology

$K$ - and $L$ -theory of the semi-direct product of the discrete 3-dimensional Heisenberg group by $ℤ / 4$ .

Lück, Wolfgang (2005)

Geometry & Topology

K-theory, flat bundles and the Borel classes

Bjørn Jahren (1999)

Fundamenta Mathematicae

Using Hausmann and Vogel's homology sphere bundle interpretation of algebraic K-theory, we construct K-theory invariants by a theory of characteristic classes for flat bundles. It is shown that the Borel classes are detected this way, as well as the rational K-theory of integer group rings of finite groups.