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- W2149384996 abstract "me, making me unfit to summarize Grothendieck’s achievement, but he appears to have associated to each X in some family of algebraic spaces a group K(X) that turns out to be a natural repository for information about X and various objects defined “over” X. Within this framework, he recovered classical Riemann-Roch as a special case of a general theorem involving K-groups. Hirzebruch and Atiyah soon realized that these ideas could be exported to the world of algebraic topology. The resulting K-theory of topological spaces— the subject of this paper— turns out to be quite powerful: among its early triumphs were Adams’ determination of the maximum number of linearly independent vector fields on S n , and the formulation and proof of the Atiyah-Singer index theorem. (Further work by many others has extended the ideas and constructions of K-theory beyond topological spaces to C -algebras and more general rings, but we will not discuss this here.)" @default.
- W2149384996 created "2016-06-24" @default.
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- W2149384996 date "2004-01-01" @default.
- W2149384996 modified "2023-09-27" @default.
- W2149384996 title "A brief glance at K-theory" @default.
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