K-theory

Abstract

K-theory was invented in the category of algebraic vector bundles over algebraic varieties by A Grothendieck, who was directly motivated by the Hirzebruch-Riemann-Roch theorem which he subsequently greatly generalized. He also defined K-homology in terms of coherent sheaves and established the basic properties of K-theory and K-homology including Poincaré duality for nonsingular varieties. The origin for the choice of the letter K in K-theory was apparently the German word "Klasse."