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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...

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.

Recollement of colimit categories and its applications

Ju Huang, QingHua Chen, Chunhuan Lai (2020)

Czechoslovak Mathematical Journal

We give an explicit recollement for a cocomplete abelian category and its colimit category. We obtain some applications on Leavitt path algebras, derived equivalences and K -groups.

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