An introduction to algebraic K-theory

Proceedings of the 20th Winter School "Geometry and Physics", GDML_Books, (2001), p. 11-28 / Harvested from

Résumé

This paper gives an exposition of algebraic K-theory, which studies functors $K_{n} : Rings \to Abelian Groups$ , $n$ 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 $\geq 5$ , 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!

MR MR1826678 | Zbl 0978.19001

EUDML-ID : urn:eudml:doc:220542
Mots clés:

@article{701666,
     title = {An introduction to algebraic K-theory},
     booktitle = {Proceedings of the 20th Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {2001},
     pages = {11-28},
     mrnumber = {MR1826678},
     zbl = {0978.19001},
     url = {http://dml.mathdoc.fr/item/701666}
}

Ausoni, Christian. An introduction to algebraic K-theory, dans Proceedings of the 20th Winter School "Geometry and Physics", GDML_Books,  (2001), pp. 11-28. http://gdmltest.u-ga.fr/item/701666/