An introduction to algebraic K-theory

Ausoni, Christian. "An introduction to algebraic K-theory." Proceedings of the 20th Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 2001. 11-28. <http://eudml.org/doc/220542>.

@inProceedings{Ausoni2001,
abstract = {This paper gives an exposition of algebraic K-theory, which studies functors $K_n:\text\{Rings\}\rightarrow \text\{Abelian Groups\}$, $n$ an integer. Classically $n=0,1$ introduced by Bass in the mid 60’s (based on ideas of Grothendieck and others) and $n=2$ introduced by Milnor [Introduction to algebraic K-theory, Annals of Math. Studies, 72, Princeton University Press, 1971: Zbl 0237.18005]. These functors are defined and applications to topological K-theory (Swan), number theory, topology and geometry (the Wall finiteness obstruction to a CW-complex being finite, Whitehead torsion which classifies $h$-cobordism for closed manifolds of dimension $\ge 5$, and the Hatcher-Wagoner theorem on pseudo-isotopy of differentiable manifolds) are briefly described. Furthermore it is explained in terms of exact sequences and products how the functors $K_i$ are connected. In the mid 1970’s Quillen, using methods of homotopy theory, introduced functors $K_n$ for $n$ an arbitrary non-neg!},
author = {Ausoni, Christian},
booktitle = {Proceedings of the 20th Winter School "Geometry and Physics"},
keywords = {Winter school; Proceedings; Geometry; Physics; Srní(Czech Republic)},
location = {Palermo},
pages = {11-28},
publisher = {Circolo Matematico di Palermo},
title = {An introduction to algebraic K-theory},
url = {http://eudml.org/doc/220542},
year = {2001},
}

TY - CLSWK
AU - Ausoni, Christian
TI - An introduction to algebraic K-theory
T2 - Proceedings of the 20th Winter School "Geometry and Physics"
PY - 2001
CY - Palermo
PB - Circolo Matematico di Palermo
SP - 11
EP - 28
AB - This paper gives an exposition of algebraic K-theory, which studies functors $K_n:\text{Rings}\rightarrow \text{Abelian Groups}$, $n$ an integer. Classically $n=0,1$ introduced by Bass in the mid 60’s (based on ideas of Grothendieck and others) and $n=2$ introduced by Milnor [Introduction to algebraic K-theory, Annals of Math. Studies, 72, Princeton University Press, 1971: Zbl 0237.18005]. These functors are defined and applications to topological K-theory (Swan), number theory, topology and geometry (the Wall finiteness obstruction to a CW-complex being finite, Whitehead torsion which classifies $h$-cobordism for closed manifolds of dimension $\ge 5$, and the Hatcher-Wagoner theorem on pseudo-isotopy of differentiable manifolds) are briefly described. Furthermore it is explained in terms of exact sequences and products how the functors $K_i$ are connected. In the mid 1970’s Quillen, using methods of homotopy theory, introduced functors $K_n$ for $n$ an arbitrary non-neg!
KW - Winter school; Proceedings; Geometry; Physics; Srní(Czech Republic)
UR - http://eudml.org/doc/220542
ER -