Thomas Hüttemann

The Fundamental Theorem for the Algebraic K-Theory of Spaces I

Abstract Let X ↦ A ( X ) denote the algebraic K -theory of spaces functor. The main objective of this paper is to show that A ( X × S 1 ) admits a functorial splitting. The splitting has four factors: a copy of A ( X ), a delooped copy of A ( X ) and two homeomorphic nil terms . One should view the decomposition as the algebraic K -theory of spaces version of the Bass-Heller-Swan theorem. In deducing this splitting, we introduce a new tool: a “non-linear” analogue of the projective line.Elsevier Science B.V.

Algebraic K-theory of non-linear projective spaces

Abstract In the spirit of “The Fundamental Theorem for the algebraic K-theory of spaces: I” (J. Pure Appl. Algebra 160 (2001) 21–52) we introduce a category of sheaves of topological spaces on n-dimensional projective space and present a calculation of its K-theory, a “non-linear” analogue of Quillens isomorphism Ki(PRn)≅⊕0nKi(R).

On Quillen's calculation of graded K-theory

We adapt Quillen’s calculation of graded

A note on the graded K-theory of certain graded rings

K

TRIANGULAR OBJECTS AND SYSTEMATIC K-THEORY

-groups of

The Fundamental Theorem for the Algebraic K-Theory of Spaces II: the Canonical Involution

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