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K-theory involves the construction of families of K-functors that map from topological spaces or schemes, or to be even more general: any object of a homotopy category to associated rings; these rings reflect some aspects of the structure of the original spaces or schemes.
Tensor product of bundles gives K-theory a commutative ring structure. Without subscripts, () usually denotes complex K-theory whereas real K-theory is sometimes written as (). The remaining discussion is focused on complex K-theory. As a first example, note that the K-theory of a point is the integers. This is because vector bundles over a ...
The K-theory classification of D-branes has had numerous applications. For example, Hanany & Kol (2000) used it to argue that there are eight species of orientifold one-plane. Uranga (2001) applied the K-theory classification to derive new consistency conditions for flux compactifications.
Download as PDF; Printable version ... Algebraic K-theory is a subject area in mathematics with connections to ... (PDF), Handbook of K-theory, Berlin, New York ...
Operator K-theory is a generalization of topological K-theory, defined by means of vector bundles on locally compact Hausdorff spaces. Here, a vector bundle over a topological space X is associated to a projection in the C* algebra of matrix-valued—that is, ()-valued—continuous functions over X.
Download as PDF; Printable version; In other projects Wikidata item; ... Pages in category "K-theory" The following 36 pages are in this category, out of 36 total.
The K-groups of finite fields are one of the few cases where the K-theory is known completely: [2] for , = (() +) {/ (), =,For n=2, this can be seen from Matsumoto's theorem, in higher degrees it was computed by Quillen in conjunction with his work on the Adams conjecture.
Download as PDF; Printable version; In other projects Wikidata item; Appearance. ... In mathematics, given a ring R, the K-theory spectrum of R is an Ω-spectrum ...