Titlebook: Algebraic K-Theory and Its Applications; Jonathan Rosenberg Textbook 1994 Springer-Verlag New York, Inc. 1994 Algebraic K-theory.Homologic

Cryptic

,The +−Construction and Quillen ,-Theory,hematics) in 1978. Quillen had the idea that one should try to construct the higher .-functors not one at a time but all at once, as the homotopy groups of a topological space (or, from a more sophisticated point of view, as the homotopy groups of a “generalized space” or “spectrum”). Thus one shoul

disciplined

Cyclic homology and its relation to ,-Theory,up . with Lie algebra ., the topological cohomology .(.ℝ) (here we are just thinking of . as a space and ignoring the group structure) is canonically isomorphic to the Lie algebra cohomology .(.ℝ), which can at least in principle be computed using only finite-dimensional linear algebra. This suggest

homeostasis

叙述

GROSS

https://doi.org/10.1007/978-3-031-32879-4hematics) in 1978. Quillen had the idea that one should try to construct the higher .-functors not one at a time but all at once, as the homotopy groups of a topological space (or, from a more sophisticated point of view, as the homotopy groups of a “generalized space” or “spectrum”). Thus one shoul

种子

Meditate

Cardiac

of Rings,, linear transformations and their invariants (determinants, canonical forms, and so on). The usual development of .-theory for rings follows the same pattern. One begins by studying projective modules and their stable classification via ., and then goes on to the study of the stable classification

吼叫

and , of Categories, Negative ,-Theory,ext, the .-theory of a ring .-theory of the category . . of finitely generated projective modules over .. Another natural example is the topological .-theory of a compact space ., which is the .-theory of the category Vect . of (locally trivial, real, or complex) vector bundles over .. The identific

旁观者

,Milnor’s ,ill seem a comforting retreat to more familiar territory. However, we will need to refer to the homology of a group, at least in order to speak of .. Since group homology will be needed in a more serious way in the next chapter anyway, we provide a brief introduction to the subject later in this sec