In mathematics, K-theory is an extraordinary cohomology theory which consists of topological K-theory and algebraic K-theory and spans the subjects of algebraic topology, abstract algebra and some areas of application like operator algebras and algebraic geometry. It leads to the construction of families of K-functors, which contain useful but often hard-to-compute information.

K-theory and physics

In string theory, K-theory has proved to be a good description of the allowed charges of D-branes. Originally the spectrum of D-brane charges was thought to be described by homology. However, the analyses of tachyon condensation (with possible non-trivial gauge fields) by Ashoke Sen has led Edward Witten to conjecture that K-theory is a better mathematical framework, and their construction was confirmed by subsequent research of many other physicists.

Related Topics:
String theory - D-branes - Homology - Tachyon condensation - Gauge field - Ashoke Sen - Edward Witten

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