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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 ...
In mathematics, Milnor K-theory [1] is an algebraic invariant (denoted () for a field) defined by John Milnor as an attempt to study higher algebraic K-theory in the special case of fields. It was hoped this would help illuminate the structure for algebraic K-theory and give some insight about its relationships with other parts of mathematics ...
Algebraic K-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called K-groups. These are groups in the sense of abstract algebra.
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; In other projects Wikidata item; ... Pages in category "K-theory" The following 36 pages are in this category, out of 36 total.
The theory K(0) agrees with singular homology with rational coefficients, whereas K(1) is a summand of mod-p complex K-theory. The theory K(n) has coefficient ring F p [v n,v n −1] where v n has degree 2(p n − 1). In particular, Morava K-theory is periodic with this period, in much the same way that complex K-theory has period 2.
Download QR code; Print/export Download as PDF; Printable version; In other projects ... Pages in category "Algebraic K-theory" The following 22 pages are in this ...